The platform used to write and generate this .html document is cat(platform) on RStudio, cat(r_info). The required packages to run all necessary code chunks are checked and installed using the pacman R package. p_load from the package is used to load and install all listed packages. The details for a number of packages are described before their use. If they are not, the .rmd file will provide the list of packages that are installed.

1 Simulating data

This section is unique only to the Stage 1 registered reported. We are not using any real data, so to ensure that each step is completed correctly, we use simulated data. We can operate under the assumption that all participants will have no missing values given how exclusion criteria are applied and fMRI data are extracted from the BOLD timeseries.

In this section, a population model is fit reflecting the theoretical phenomenon that are involved in the reward processing construct. The idea is that there are approach and avoidance (measured constructs) characteristics that are associated with stimuli within/across tasks (Manifest variables). There is no ground truth of these processes at the individual. Nevertheless, the variables are important to the broad construct of approach and avoidance that are sub-constructs of the higher-order reward processing construct. In the MID task these constructs are hypothesized to reflect the the multidimensional affective circumplex model. As formalized here, in the MID task the contrasts reflect the manifest variables (i.e., reflective model) as opposed of the other way, whereby the items form the variables predict the construct (i.e., formative model).

1.1 Specify Population Model

Start off by specifying the population model. In this scenario, the individual runs load onto the specific Contrast and ROI combinations. Then, the ROIs are loaded onto the factors approach and avoidance. The approach and avoidance are specified as negatively correlated and the factor variances are fixed to 1. This is because in the multidimensional circumplex model, when the span of the contrasts are considered, these measures will likely not be orthogonal but instead >90 degree in space.

population_model<-'
# By run loadings for bilateral regions
AWin_v_Neut_L_NAcc =~     .7*AWin_v_Neut_L_NAcc_run1    + .7*AWin_v_Neut_L_NAcc_run2
AWin_v_Neut_L_Insula =~   .7*AWin_v_Neut_L_Insula_run1  + .7*AWin_v_Neut_L_Insula_run2
BWin_v_Neut_L_NAcc =~     .7*BWin_v_Neut_L_NAcc_run1    + .7*BWin_v_Neut_L_NAcc_run2
BWin_v_Neut_L_Insula =~   .7*BWin_v_Neut_L_Insula_run1  + .7*BWin_v_Neut_L_Insula_run2
BWin_v_BLose_L_NAcc =~    .7*BWin_v_BLose_L_NAcc_run1   + .7*BWin_v_BLose_L_NAcc_run2
BWin_v_BLose_L_Insula =~  .7*BWin_v_BLose_L_Insula_run1 + .7*BWin_v_BLose_L_Insula_run2
ALose_v_Neut_L_NAcc =~    .7*ALose_v_Neut_L_NAcc_run1   + .7*ALose_v_Neut_L_NAcc_run2
ALose_v_Neut_L_Insula =~  .7*ALose_v_Neut_L_Insula_run1 + .7*ALose_v_Neut_L_Insula_run2
BLose_v_Neut_L_NAcc =~    .7*BLose_v_Neut_L_NAcc_run1   + .7*BLose_v_Neut_L_NAcc_run2
BLose_v_Neut_L_Insula =~  .7*BLose_v_Neut_L_Insula_run1 + .7*BLose_v_Neut_L_Insula_run2
BLose_v_BWin_L_NAcc =~    .7*BLose_v_BWin_L_NAcc_run1   + .7*BLose_v_BWin_L_NAcc_run2
BLose_v_BWin_L_Insula =~  .7*BLose_v_BWin_L_Insula_run1 + .7*BLose_v_BWin_L_Insula_run2

AWin_v_Neut_R_NAcc =~     .7*AWin_v_Neut_R_NAcc_run1    + .7*AWin_v_Neut_R_NAcc_run2
AWin_v_Neut_R_Insula =~   .7*AWin_v_Neut_R_Insula_run1  + .7*AWin_v_Neut_R_Insula_run2
BWin_v_Neut_R_NAcc =~     .7*BWin_v_Neut_R_NAcc_run1    + .7*BWin_v_Neut_R_NAcc_run2
BWin_v_Neut_R_Insula =~   .7*BWin_v_Neut_R_Insula_run1  + .7*BWin_v_Neut_R_Insula_run2
BWin_v_BLose_R_NAcc =~    .7*BWin_v_BLose_R_NAcc_run1   + .7*BWin_v_BLose_R_NAcc_run2
BWin_v_BLose_R_Insula =~  .7*BWin_v_BLose_R_Insula_run1 + .7*BWin_v_BLose_R_Insula_run2
ALose_v_Neut_R_NAcc =~    .7*ALose_v_Neut_R_NAcc_run1   + .7*ALose_v_Neut_R_NAcc_run2
ALose_v_Neut_R_Insula =~  .7*ALose_v_Neut_R_Insula_run1 + .7*ALose_v_Neut_R_Insula_run2
BLose_v_Neut_R_NAcc =~    .7*BLose_v_Neut_R_NAcc_run1   + .7*BLose_v_Neut_R_NAcc_run2
BLose_v_Neut_R_Insula =~  .7*BLose_v_Neut_R_Insula_run1 + .7*BLose_v_Neut_R_Insula_run2
BLose_v_BWin_R_NAcc =~    .7*BLose_v_BWin_R_NAcc_run1   + .7*BLose_v_BWin_R_NAcc_run2
BLose_v_BWin_R_Insula =~  .7*BLose_v_BWin_R_Insula_run1 + .7*BLose_v_BWin_R_Insula_run2

#Factor item loadings 
Approach =~  .8*AWin_v_Neut_L_NAcc + .8*AWin_v_Neut_R_NAcc + .45*AWin_v_Neut_R_Insula +
            .7*BWin_v_Neut_L_NAcc +   .7*BWin_v_Neut_R_NAcc + .4*BWin_v_Neut_R_Insula +
            .8*BWin_v_BLose_L_NAcc +  .8*BWin_v_BLose_R_NAcc
                
Avoid =~  .8*ALose_v_Neut_L_Insula  + .8*ALose_v_Neut_R_Insula +
          .75*BLose_v_Neut_L_Insula + .75*BLose_v_Neut_R_Insula +
          .8*BLose_v_BWin_L_Insula  + .45*BLose_v_BWin_R_Insula
            
# Factor Covariances 
Approach ~~ -.6*Avoid

# Fixing factor variances
Approach ~~ 1*Approach
Avoid ~~ 1*Avoid

'

1.2 General samples

Using the population model, simsem is used to create simulated data. This generates a fake dataset that is used to pilot the planned Mutligroup CFA, ESEM, EFA and Local SEM models

In this case, 50 repetitions are simulated per model for an approximate N sample for each study. Even though the factor variances are specified in the population model as ‘1’, this model fixeds all latent variables using std.lv = TRUE.

  1. AHRB N = 108
  2. MLS N = 159
  3. ABCD N = 1000
set.seed(25151215)
sim_AHRB <- simsem::sim(nRep = 50, model = "lavaan", n = 108, 
           generate = population_model, std.lv = TRUE, lavaanfun = "sem", 
           # std.lv ~ ix the variances of all the latent variables 
           dataOnly=T, meanstructure = FALSE, seed=123)

sim_MLS <- simsem::sim(nRep = 50, model = "lavaan", n = 159, 
                generate = population_model, std.lv = TRUE, lavaanfun = "sem", 
                dataOnly=T, meanstructure = FALSE, seed=123)

sim_ABCD <- simsem::sim(nRep = 50, model = "lavaan", n = 1000, 
               generate = population_model, std.lv = TRUE, lavaanfun = "sem", 
               dataOnly=T, meanstructure = FALSE, seed=123)

Average each repetition for each simulated sample. For example, after 50 repetitions of 1000 participants for the population model of ABCD sample, an average estimate is derived using aaply. For each study, the set variable is created to differentiate which sample the data is associated with (i.e., grouping variable). In this case, AHRB = 3, MLS = 2, ABCD = 1.

sim_AHRB_data <- data.frame(aaply(laply(sim_AHRB, as.matrix), c(2,3), mean))
  sim_AHRB_data$set <-3
  
sim_MLS_data <- data.frame(aaply(laply(sim_MLS, as.matrix), c(2,3), mean))
  sim_MLS_data$set <-2
  
sim_ABCD_data <- data.frame(aaply(laply(sim_ABCD, as.matrix), c(2,3), mean))
  sim_ABCD_data$set <-1

Next, row bind the data sets to form one complete data. This equivalent to stacking the datasets and only retaining a single header row (since all variable names are constant). This creates a 1267 x 49 data matrix (48 brain variables + sample label)

brain_set <- rbind(sim_AHRB_data,sim_MLS_data,sim_ABCD_data)

1.3 Correlation matrix of data

Here, a combination of rcorr and corrplot are used to visualize the associations among the brain variables in the dataset.

# Using Hmisc to create a 24x24 matrix for a list (3) that contains: the pearson's r corr, sample size (N), and significance (p).
Brain_corr = rcorr(as.matrix(subset(brain_set,select=-c(set))), # excluding the set of data related to sample
                   type = "pearson")


# Using corrplot() to create heatmap of the data. 
par(mfrow=c(1,1))
corrplot(Brain_corr$r, type = "upper", 
         order = 'hclust',
         method =  "color", 
         tl.cex = 0.5, tl.col = 'black',
         cl.pos = 'r', tl.pos = 'lt', outline = TRUE,
         col=colorRampPalette(c("navyblue","white","red2"))(100),# colours http://www.stat.columbia.edu/~tzheng/files/Rcolor.pdf
         mar = c(2,.15,.25,.15)#bottom, left, top and right,
         )

2 Running [restricted] Multigroup CFA

Run the CFA multi-group analysis for the three datasets. Multi-group CFA tests the measurement invariance across defined groups to determine whether soft and strict invariance criteria are met and the degree to which the derive estimates for an item in one study can be compared to the same item in another sample. In this case, the focus is on the configural (structure) and metric invariance (loadings). In short, this model evaluates whether factor structure and loadings for the approach and avoidance model are invariant (dont significant differ) across the samples.

Code here is based on measurement invariance models from Maasen et al. 2019, Measurement invariance presentation from Kate Xu and Multi-group CFA tutorial from Hirschfeld & Brachel (2014).

The issue of multi-group is invariance what is discussed in Borsboom (2006). In short, (1) Interpretation of group differences on observed scores DEPENDS on the invariance of measurement models & (2) many make conclusions without doing a single test of measurement invariance.

A tutorial on CFA broadly is available from Lizbeth Benzon and Nilam Ram here and tutorial of measurement invariance (in context of longitudinal data) from Nilam Ram is available here

2.1 CFA model

The below specified model will be used. The number of estimate parameters are fewer and may be more appropriate for the theoretical model. This model may result in few convergence issues if the number of participants ends up to be few and the coefficients/estimates are lower.(see Kline 2015 book on Principles and Practice of Structural Equation Modeling).

MID_model <-'

# Factor loadings
Approach =~ AWin_v_Neut_L_NAcc_run1  + AWin_v_Neut_R_NAcc_run1  + AWin_v_Neut_R_Insula_run1 +
            AWin_v_Neut_L_NAcc_run2  + AWin_v_Neut_R_NAcc_run2 + AWin_v_Neut_R_Insula_run2 +
            BWin_v_Neut_L_NAcc_run1  + BWin_v_Neut_R_NAcc_run1  + BWin_v_Neut_R_Insula_run1 +
            BWin_v_Neut_L_NAcc_run2  + BWin_v_Neut_R_NAcc_run2  + BWin_v_Neut_R_Insula_run2 +
            BWin_v_BLose_L_NAcc_run1 + BWin_v_BLose_R_NAcc_run1 +
            BWin_v_BLose_L_NAcc_run2 + BWin_v_BLose_R_NAcc_run2 
                
Avoid =~    ALose_v_Neut_L_Insula_run1 + ALose_v_Neut_R_Insula_run1 +
            ALose_v_Neut_L_Insula_run2 + ALose_v_Neut_R_Insula_run2 +
            BLose_v_Neut_L_Insula_run1 + BLose_v_Neut_R_Insula_run1 +
            BLose_v_Neut_L_Insula_run2 + BLose_v_Neut_R_Insula_run2 +
            BLose_v_BWin_L_Insula_run1 + BLose_v_BWin_R_Insula_run1 +
            BLose_v_BWin_L_Insula_run2 + BLose_v_BWin_R_Insula_run2 
'

2.2 Running CFA: Three Samples

Below is the CFA model that is used to test the proposed restricted model (see Figure 1 in the manuscript). The CFA fitting procedure is consistent with the description here. For each CFA model, the full sample is filtered for each type sample, e.g. AHRB, MLS, ABCD. The std.lv= = TRUE constrain the latent factor variances to 1. The estimator being used is MLR, a maximum likelihood robust estimator. A CFA model is estimated for the complete data (i.e., all three datasets).

all_sample <- cfa(model = MID_model, data = brain_set,
               estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

2.3 Fitting Configural CFA

Here, the configular multigroup model is fit. As described in D’Urso et al. (2022) measurement invariance pre-print, the configural model tests:

is the structure of the factors is invariannt across the samples (‘set’). In other words, if we a priori propose a two-factor structure (FA 1 = approch and FA 2 = Avoidance), does this two factor structure represent the between-person variability in the items that reflect the factors across each sample?

If the variability in one sample suggests a one, three, or four factor structure, this will be degrade the fit statistics.

A pre-specified CFA model is used to evaluate whether the measures/items that reflect the factor are the same across groups. group= 'set' is used to define the grouping variable. All loadings and intercepts are free to vary across groups, and the factor variance is set to ‘1’ via std.lv = TRUE

configural_cfa <- cfa(model = MID_model, data = brain_set, group = 'set', 
                      estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

2.4 Fitting Metric CFA

After fitting the CFA configurial (factor structure) invariance, if the model fit is not poor, then the next step is to test the metric invariance. Metric invariance tests:

are the loadings are consistent across the groups. In other words,are the phenomena (i.e., approach and avoidance) reflected by the same pattern across the measures/items?

One cause for concern may be that the phenomenon are not invariant across age groups, in that the items/measures (ROIs for a given contrast) do not load in the same manner onto each factor. This ‘soft’ measure of invariance can determine whether the items functions differ across the items and so cannot be easily compared.

The model is fit using the same procedure as for configurial invariance with one exception: In metric invariance the loadings group equality constraint is added to the model via group.equal=c("loadings"). The model fit statistics are used to evaluate whether the fit is poor.

metric_cfa <-cfa(model = MID_model, data = brain_set, 
                 group = 'set', group.equal=c("loadings"),
                 estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

2.5 Extracting Fit Statistics

Once the above models are fit, the following information is pulled out and saved into a out data frame:

  1. Model name
  2. Chi-square statistics
  3. Model Degrees of Freedom (df)
  4. Model p-value
  5. RMSEA
  6. CFI
  7. SRMR
  8. AIC
  9. BIC
# Below selects specific fit data as described in Maassen et al. 2019 OSF. No comparisons are made to compare models at this point.
out <- matrix(NA, ncol = 10, nrow = 4)
colnames(out) <- c("model","chisq","df","pvalue", "rmsea", "cfi","tli", "srmr",
                   "AIC", "BIC")

# save fit measures from models
out[1,2:8] <- round(data.matrix(fitmeasures(all_sample, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi","tli", "srmr"))), 
                    digits=3)

out[2,2:8] <- round(data.matrix(fitmeasures(configural_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi","tli", "srmr"))), 
                            digits=3)

out[3,2:8] <- round(data.matrix(fitmeasures(metric_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi","tli", "srmr"))), 
                    digits=3)


# AIC models
out[1,9] <- round(AIC(all_sample),3)
out[2,9] <- round(AIC(configural_cfa),3)
out[3,9] <- round(AIC(metric_cfa),3)

# BIC models
out[1,10] <- round(BIC(all_sample),3)
out[2,10] <- round(BIC(configural_cfa),3)
out[3,10] <- round(BIC(metric_cfa),3)

out[1:3,1] <-  c("Overall CFA", "Configg MG-CFA", "Metric MG-CFA")

2.6 Model Parameter Summary

Reporting standardized coefficients.

2.6.1 All Sample CFA model

##### Summarizing All Samples CFA model #####
parameters(all_sample, standardize = T)
## # Loading
## 
## Link                                  | Coefficient |   SE |       95% CI |     z |      p
## ------------------------------------------------------------------------------------------
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.44 | 0.03 | [0.38, 0.51] | 14.45 | < .001
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.45 | 0.03 | [0.40, 0.51] | 15.78 | < .001
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.22 | 0.03 | [0.16, 0.29] |  7.08 | < .001
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.48 | 0.03 | [0.43, 0.54] | 16.93 | < .001
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.48 | 0.03 | [0.43, 0.53] | 17.82 | < .001
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.24 | 0.03 | [0.17, 0.30] |  7.47 | < .001
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.48 | 0.03 | [0.42, 0.53] | 17.17 | < .001
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.37 | 0.03 | [0.31, 0.43] | 12.53 | < .001
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.23 | 0.03 | [0.17, 0.29] |  7.32 | < .001
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.40 | 0.03 | [0.35, 0.46] | 13.99 | < .001
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.41 | 0.03 | [0.36, 0.47] | 14.73 | < .001
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.27 | 0.03 | [0.21, 0.33] |  8.30 | < .001
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.45 | 0.03 | [0.39, 0.50] | 15.12 | < .001
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.47 | 0.03 | [0.41, 0.53] | 16.47 | < .001
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.42 | 0.03 | [0.37, 0.48] | 14.19 | < .001
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.47 | 0.03 | [0.42, 0.53] | 16.34 | < .001
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.46 | 0.03 | [0.40, 0.52] | 15.36 | < .001
## Avoid =~ ALose_v_Neut_R_Insula_run1   |        0.48 | 0.03 | [0.42, 0.53] | 16.58 | < .001
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.42 | 0.03 | [0.36, 0.48] | 14.25 | < .001
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.47 | 0.03 | [0.41, 0.52] | 16.74 | < .001
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.44 | 0.03 | [0.38, 0.50] | 14.51 | < .001
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.50 | 0.03 | [0.44, 0.56] | 16.42 | < .001
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.41 | 0.03 | [0.35, 0.47] | 13.36 | < .001
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.48 | 0.03 | [0.43, 0.54] | 16.06 | < .001
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.45 | 0.03 | [0.40, 0.51] | 14.94 | < .001
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.27 | 0.03 | [0.21, 0.34] |  8.55 | < .001
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.45 | 0.03 | [0.39, 0.51] | 14.91 | < .001
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.27 | 0.03 | [0.21, 0.34] |  8.53 | < .001
## 
## # Correlation
## 
## Link              | Coefficient |   SE |         95% CI |      z |      p
## -------------------------------------------------------------------------
## Approach ~~ Avoid |       -0.55 | 0.03 | [-0.61, -0.49] | -18.77 | < .001

2.6.2 Configural CFA model

##### Summarizing Configural MG-CFA model #####
parameters(configural_cfa, standardize = T)
## # Loading
## 
## Link                                  | Coefficient |   SE |        95% CI |     z |      p | Group
## ---------------------------------------------------------------------------------------------------
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.51 | 0.13 | [ 0.26, 0.76] |  4.03 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.51 | 0.10 | [ 0.31, 0.71] |  5.07 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.19 | 0.13 | [-0.07, 0.45] |  1.43 | 0.154  |  1.00
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.47 | 0.13 | [ 0.21, 0.72] |  3.63 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.38 | 0.12 | [ 0.15, 0.61] |  3.23 | 0.001  |  1.00
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.18 | 0.14 | [-0.09, 0.45] |  1.29 | 0.198  |  1.00
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.33 | 0.11 | [ 0.12, 0.54] |  3.12 | 0.002  |  1.00
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.30 | 0.15 | [ 0.01, 0.59] |  2.00 | 0.046  |  1.00
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.10 | 0.14 | [-0.16, 0.37] |  0.76 | 0.445  |  1.00
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.34 | 0.10 | [ 0.14, 0.55] |  3.28 | 0.001  |  1.00
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.45 | 0.11 | [ 0.25, 0.66] |  4.30 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.26 | 0.11 | [ 0.04, 0.48] |  2.27 | 0.023  |  1.00
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.34 | 0.14 | [ 0.07, 0.61] |  2.45 | 0.014  |  1.00
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.48 | 0.10 | [ 0.29, 0.67] |  4.94 | < .001 |  1.00
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.44 | 0.15 | [ 0.14, 0.73] |  2.88 | 0.004  |  1.00
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.56 | 0.09 | [ 0.38, 0.75] |  6.06 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.52 | 0.10 | [ 0.32, 0.72] |  5.16 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_R_Insula_run1   |        0.53 | 0.09 | [ 0.34, 0.71] |  5.62 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.55 | 0.11 | [ 0.33, 0.77] |  4.86 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.54 | 0.10 | [ 0.34, 0.73] |  5.33 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.50 | 0.10 | [ 0.30, 0.69] |  4.95 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.41 | 0.10 | [ 0.21, 0.61] |  3.99 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.23 | 0.09 | [ 0.05, 0.41] |  2.54 | 0.011  |  1.00
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.46 | 0.11 | [ 0.24, 0.68] |  4.11 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.34 | 0.10 | [ 0.15, 0.53] |  3.52 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.37 | 0.09 | [ 0.19, 0.56] |  3.98 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.41 | 0.12 | [ 0.17, 0.64] |  3.38 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.37 | 0.10 | [ 0.17, 0.57] |  3.61 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.42 | 0.10 | [ 0.22, 0.61] |  4.23 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.54 | 0.07 | [ 0.40, 0.69] |  7.43 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.15 | 0.08 | [-0.01, 0.31] |  1.89 | 0.059  |  2.00
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.51 | 0.08 | [ 0.36, 0.67] |  6.55 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.41 | 0.09 | [ 0.23, 0.59] |  4.52 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Insula_run2 |    2.85e-03 | 0.09 | [-0.18, 0.18] |  0.03 | 0.975  |  2.00
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.40 | 0.11 | [ 0.19, 0.61] |  3.73 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.32 | 0.10 | [ 0.11, 0.52] |  3.04 | 0.002  |  2.00
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.23 | 0.10 | [ 0.03, 0.44] |  2.23 | 0.026  |  2.00
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.31 | 0.10 | [ 0.12, 0.49] |  3.23 | 0.001  |  2.00
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.33 | 0.09 | [ 0.16, 0.50] |  3.80 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.27 | 0.10 | [ 0.08, 0.47] |  2.74 | 0.006  |  2.00
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.37 | 0.10 | [ 0.17, 0.56] |  3.71 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.51 | 0.08 | [ 0.35, 0.67] |  6.29 | < .001 |  2.00
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.44 | 0.09 | [ 0.27, 0.61] |  5.10 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.36 | 0.09 | [ 0.19, 0.54] |  3.99 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.51 | 0.08 | [ 0.34, 0.67] |  6.14 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_R_Insula_run1   |        0.37 | 0.09 | [ 0.20, 0.53] |  4.24 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.39 | 0.09 | [ 0.22, 0.56] |  4.38 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.51 | 0.07 | [ 0.38, 0.64] |  7.65 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.35 | 0.08 | [ 0.19, 0.51] |  4.24 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.50 | 0.07 | [ 0.35, 0.64] |  6.64 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.44 | 0.07 | [ 0.30, 0.58] |  6.24 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.47 | 0.09 | [ 0.31, 0.64] |  5.55 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.61 | 0.08 | [ 0.46, 0.76] |  7.97 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.48 | 0.07 | [ 0.33, 0.62] |  6.40 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.63 | 0.06 | [ 0.50, 0.75] |  9.85 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.44 | 0.08 | [ 0.29, 0.59] |  5.74 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.45 | 0.03 | [ 0.38, 0.51] | 13.11 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.43 | 0.03 | [ 0.37, 0.50] | 13.35 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.24 | 0.04 | [ 0.17, 0.31] |  6.69 | < .001 |  3.00
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.48 | 0.03 | [ 0.42, 0.55] | 14.87 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.49 | 0.03 | [ 0.44, 0.55] | 17.00 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.27 | 0.03 | [ 0.20, 0.34] |  7.91 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.51 | 0.03 | [ 0.45, 0.56] | 16.98 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.39 | 0.03 | [ 0.32, 0.45] | 12.10 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.24 | 0.03 | [ 0.17, 0.31] |  6.99 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.42 | 0.03 | [ 0.36, 0.48] | 13.20 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.42 | 0.03 | [ 0.36, 0.48] | 13.55 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.27 | 0.04 | [ 0.20, 0.35] |  7.45 | < .001 |  3.00
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.47 | 0.03 | [ 0.41, 0.53] | 15.00 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.46 | 0.03 | [ 0.40, 0.53] | 14.42 | < .001 |  3.00
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.42 | 0.03 | [ 0.36, 0.48] | 12.84 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.48 | 0.03 | [ 0.42, 0.55] | 14.99 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.44 | 0.03 | [ 0.38, 0.51] | 12.82 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_R_Insula_run1   |        0.50 | 0.03 | [ 0.43, 0.56] | 15.48 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.41 | 0.03 | [ 0.34, 0.47] | 12.44 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.46 | 0.03 | [ 0.39, 0.52] | 14.14 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.44 | 0.03 | [ 0.38, 0.51] | 12.90 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.51 | 0.03 | [ 0.44, 0.57] | 14.46 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.43 | 0.04 | [ 0.36, 0.50] | 11.76 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.48 | 0.03 | [ 0.42, 0.55] | 14.05 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.44 | 0.03 | [ 0.37, 0.51] | 12.62 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.23 | 0.04 | [ 0.16, 0.30] |  6.18 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.42 | 0.04 | [ 0.35, 0.49] | 11.89 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.23 | 0.04 | [ 0.16, 0.31] |  6.25 | < .001 |  3.00
## 
## # Correlation
## 
## Link              | Coefficient |   SE |         95% CI |      z |      p | Group
## ---------------------------------------------------------------------------------
## Approach ~~ Avoid |       -0.42 | 0.12 | [-0.65, -0.19] |  -3.63 | < .001 |  1.00
## Approach ~~ Avoid |       -0.54 | 0.09 | [-0.71, -0.36] |  -6.01 | < .001 |  2.00
## Approach ~~ Avoid |       -0.57 | 0.03 | [-0.63, -0.51] | -17.66 | < .001 |  3.00

2.6.3 Metric CFA model

##### Summarizing Metric Multi-group CFA model #####
parameters(metric_cfa, standardize = T)
## # Loading
## 
## Link                                          | Coefficient |   SE |       95% CI |     z |      p | Group
## ----------------------------------------------------------------------------------------------------------
## Approach =~ AWin_v_Neut_L_NAcc_run1 (.p1.)    |        0.43 | 0.05 | [0.33, 0.53] |  8.39 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAcc_run1 (.p2.)    |        0.43 | 0.06 | [0.32, 0.54] |  7.56 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Insula_run1 (.p3.)  |        0.20 | 0.04 | [0.13, 0.27] |  5.63 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAcc_run2 (.p4.)    |        0.46 | 0.05 | [0.36, 0.56] |  9.09 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAcc_run2 (.p5.)    |        0.46 | 0.05 | [0.36, 0.55] |  9.65 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Insula_run2 (.p6.)  |        0.23 | 0.04 | [0.14, 0.31] |  5.41 | < .001 |  1.00
## Approach =~ BWin_v_Neut_L_NAcc_run1 (.p7.)    |        0.43 | 0.05 | [0.34, 0.53] |  8.94 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_NAcc_run1 (.p8.)    |        0.36 | 0.05 | [0.26, 0.45] |  7.54 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Insula_run1 (.p9.)  |        0.22 | 0.04 | [0.15, 0.30] |  5.99 | < .001 |  1.00
## Approach =~ BWin_v_Neut_L_NAcc_run2 (.p10.)   |        0.39 | 0.05 | [0.30, 0.48] |  8.24 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_NAcc_run2 (.p11.)   |        0.38 | 0.05 | [0.28, 0.47] |  7.77 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Insula_run2 (.p12.) |        0.29 | 0.04 | [0.20, 0.38] |  6.53 | < .001 |  1.00
## Approach =~ BWin_v_BLose_L_NAcc_run1 (.p13.)  |        0.40 | 0.05 | [0.31, 0.49] |  8.48 | < .001 |  1.00
## Approach =~ BWin_v_BLose_R_NAcc_run1 (.p14.)  |        0.45 | 0.05 | [0.36, 0.55] |  9.18 | < .001 |  1.00
## Approach =~ BWin_v_BLose_L_NAcc_run2 (.p15.)  |        0.36 | 0.05 | [0.27, 0.45] |  7.80 | < .001 |  1.00
## Approach =~ BWin_v_BLose_R_NAcc_run2 (.p16.)  |        0.50 | 0.06 | [0.38, 0.61] |  8.40 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Insula_run1 (.p17.)   |        0.47 | 0.05 | [0.37, 0.57] |  9.59 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_R_Insula_run1 (.p18.)   |        0.48 | 0.05 | [0.38, 0.58] |  9.33 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Insula_run2 (.p19.)   |        0.41 | 0.05 | [0.32, 0.51] |  8.48 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_R_Insula_run2 (.p20.)   |        0.44 | 0.05 | [0.34, 0.54] |  8.57 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_L_Insula_run1 (.p21.)   |        0.46 | 0.05 | [0.36, 0.55] |  9.63 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Insula_run1 (.p22.)   |        0.48 | 0.04 | [0.39, 0.57] | 10.63 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_L_Insula_run2 (.p23.)   |        0.40 | 0.04 | [0.32, 0.49] |  9.31 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Insula_run2 (.p24.)   |        0.51 | 0.05 | [0.41, 0.61] | 10.19 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Insula_run1 (.p25.)   |        0.48 | 0.04 | [0.39, 0.56] | 11.05 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Insula_run1 (.p26.)   |        0.30 | 0.04 | [0.21, 0.39] |  6.78 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Insula_run2 (.p27.)   |        0.47 | 0.05 | [0.37, 0.56] |  9.97 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Insula_run2 (.p28.)   |        0.28 | 0.04 | [0.19, 0.36] |  6.44 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAcc_run1 (.p1.)    |        0.42 | 0.04 | [0.33, 0.50] |  9.65 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAcc_run1 (.p2.)    |        0.44 | 0.05 | [0.34, 0.53] |  9.03 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Insula_run1 (.p3.)  |        0.22 | 0.03 | [0.15, 0.29] |  6.46 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAcc_run2 (.p4.)    |        0.44 | 0.04 | [0.35, 0.52] | 10.49 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAcc_run2 (.p5.)    |        0.44 | 0.04 | [0.37, 0.52] | 10.97 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Insula_run2 (.p6.)  |        0.22 | 0.03 | [0.16, 0.28] |  7.38 | < .001 |  2.00
## Approach =~ BWin_v_Neut_L_NAcc_run1 (.p7.)    |        0.42 | 0.04 | [0.34, 0.51] | 10.00 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAcc_run1 (.p8.)    |        0.32 | 0.04 | [0.25, 0.40] |  8.44 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Insula_run1 (.p9.)  |        0.20 | 0.03 | [0.14, 0.27] |  6.20 | < .001 |  2.00
## Approach =~ BWin_v_Neut_L_NAcc_run2 (.p10.)   |        0.38 | 0.04 | [0.30, 0.45] |  9.46 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAcc_run2 (.p11.)   |        0.36 | 0.04 | [0.28, 0.44] |  9.06 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Insula_run2 (.p12.) |        0.24 | 0.04 | [0.17, 0.32] |  6.51 | < .001 |  2.00
## Approach =~ BWin_v_BLose_L_NAcc_run1 (.p13.)  |        0.41 | 0.04 | [0.33, 0.48] | 10.32 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAcc_run1 (.p14.)  |        0.45 | 0.04 | [0.36, 0.54] | 10.14 | < .001 |  2.00
## Approach =~ BWin_v_BLose_L_NAcc_run2 (.p15.)  |        0.37 | 0.04 | [0.29, 0.45] |  9.01 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAcc_run2 (.p16.)  |        0.41 | 0.04 | [0.33, 0.49] | 10.34 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_L_Insula_run1 (.p17.)   |        0.48 | 0.05 | [0.39, 0.57] | 10.43 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_R_Insula_run1 (.p18.)   |        0.50 | 0.04 | [0.43, 0.58] | 13.51 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_L_Insula_run2 (.p19.)   |        0.44 | 0.04 | [0.36, 0.53] | 10.74 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_R_Insula_run2 (.p20.)   |        0.53 | 0.04 | [0.45, 0.61] | 12.91 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_L_Insula_run1 (.p21.)   |        0.45 | 0.04 | [0.37, 0.53] | 11.26 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Insula_run1 (.p22.)   |        0.56 | 0.04 | [0.48, 0.64] | 13.66 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_L_Insula_run2 (.p23.)   |        0.46 | 0.04 | [0.38, 0.55] | 10.64 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Insula_run2 (.p24.)   |        0.52 | 0.04 | [0.43, 0.60] | 12.04 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Insula_run1 (.p25.)   |        0.51 | 0.05 | [0.42, 0.60] | 10.92 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_R_Insula_run1 (.p26.)   |        0.33 | 0.05 | [0.23, 0.43] |  6.59 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Insula_run2 (.p27.)   |        0.50 | 0.05 | [0.40, 0.59] | 10.01 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_R_Insula_run2 (.p28.)   |        0.28 | 0.04 | [0.20, 0.36] |  6.93 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAcc_run1 (.p1.)    |        0.45 | 0.03 | [0.39, 0.51] | 14.42 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAcc_run1 (.p2.)    |        0.46 | 0.03 | [0.40, 0.51] | 15.97 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Insula_run1 (.p3.)  |        0.23 | 0.03 | [0.16, 0.29] |  7.03 | < .001 |  3.00
## Approach =~ AWin_v_Neut_L_NAcc_run2 (.p4.)    |        0.49 | 0.03 | [0.43, 0.55] | 16.52 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAcc_run2 (.p5.)    |        0.48 | 0.03 | [0.43, 0.54] | 17.30 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Insula_run2 (.p6.)  |        0.24 | 0.03 | [0.17, 0.30] |  7.16 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAcc_run1 (.p7.)    |        0.50 | 0.03 | [0.44, 0.55] | 17.20 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAcc_run1 (.p8.)    |        0.38 | 0.03 | [0.32, 0.44] | 12.64 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Insula_run1 (.p9.)  |        0.24 | 0.03 | [0.17, 0.30] |  7.28 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAcc_run2 (.p10.)   |        0.41 | 0.03 | [0.35, 0.47] | 13.61 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAcc_run2 (.p11.)   |        0.42 | 0.03 | [0.37, 0.48] | 14.80 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Insula_run2 (.p12.) |        0.27 | 0.03 | [0.21, 0.34] |  8.27 | < .001 |  3.00
## Approach =~ BWin_v_BLose_L_NAcc_run1 (.p13.)  |        0.46 | 0.03 | [0.40, 0.52] | 15.10 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAcc_run1 (.p14.)  |        0.47 | 0.03 | [0.42, 0.53] | 16.39 | < .001 |  3.00
## Approach =~ BWin_v_BLose_L_NAcc_run2 (.p15.)  |        0.43 | 0.03 | [0.37, 0.49] | 14.26 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAcc_run2 (.p16.)  |        0.49 | 0.03 | [0.43, 0.54] | 16.43 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Insula_run1 (.p17.)   |        0.46 | 0.03 | [0.40, 0.52] | 15.12 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_R_Insula_run1 (.p18.)   |        0.47 | 0.03 | [0.41, 0.53] | 15.57 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Insula_run2 (.p19.)   |        0.42 | 0.03 | [0.36, 0.48] | 14.03 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_R_Insula_run2 (.p20.)   |        0.46 | 0.03 | [0.40, 0.51] | 16.08 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_L_Insula_run1 (.p21.)   |        0.43 | 0.03 | [0.37, 0.49] | 13.74 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Insula_run1 (.p22.)   |        0.49 | 0.03 | [0.42, 0.55] | 15.06 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_L_Insula_run2 (.p23.)   |        0.40 | 0.03 | [0.34, 0.47] | 12.48 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Insula_run2 (.p24.)   |        0.47 | 0.03 | [0.41, 0.53] | 15.11 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Insula_run1 (.p25.)   |        0.44 | 0.03 | [0.38, 0.51] | 14.04 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Insula_run1 (.p26.)   |        0.27 | 0.03 | [0.21, 0.33] |  8.91 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Insula_run2 (.p27.)   |        0.44 | 0.03 | [0.38, 0.50] | 14.73 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Insula_run2 (.p28.)   |        0.27 | 0.03 | [0.21, 0.33] |  8.55 | < .001 |  3.00
## 
## # Correlation
## 
## Link              | Coefficient |   SE |         95% CI |      z |      p | Group
## ---------------------------------------------------------------------------------
## Approach ~~ Avoid |       -0.40 | 0.11 | [-0.62, -0.18] |  -3.61 | < .001 |  1.00
## Approach ~~ Avoid |       -0.53 | 0.09 | [-0.71, -0.36] |  -6.03 | < .001 |  2.00
## Approach ~~ Avoid |       -0.57 | 0.03 | [-0.64, -0.51] | -17.75 | < .001 |  3.00

2.7 Comparing models w/ BIC/AIC (anova)

The below compares whether the complete data (across all three samples) in the all_cfa model is significantly improved by the configural invariance model. A significant value indicates that the configural model is significantly better than the full sample cfa.

anova(all_sample, configural_cfa)
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan NOTE:
##     The "Chisq" column contains standard test statistics, not the
##     robust test that should be reported per model. A robust difference
##     test is a function of two standard (not robust) statistics.
##  
##                  Df    AIC    BIC  Chisq Chisq diff Df diff Pr(>Chisq)  
## all_sample      349 -21672 -21235 2200.6                                
## configural_cfa 1047 -21482 -20170 2961.4     777.17     698    0.01964 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Next, anova is used to compare the model improve in AIC/BIC by between the configural and metric invariance. A significantly result in the anova would indicate a significant improvement of the metric model over the configural model.

anova(configural_cfa, metric_cfa)
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan NOTE:
##     The "Chisq" column contains standard test statistics, not the
##     robust test that should be reported per model. A robust difference
##     test is a function of two standard (not robust) statistics.
##  
##                  Df    AIC    BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## configural_cfa 1047 -21482 -20170 2961.4                              
## metric_cfa     1099 -21523 -20479 3024.3     53.862      52      0.403

2.8 Plotting multi-group config. CFA

Use semPaths to plot the configural invariance CFA multigroup model

# this plottinig is not function with runs loading onto ROIs

layout(t(1:3))
semPaths(configural_cfa,
         color = "lightyellow",
         theme="colorblind",
         whatLabels = "std",
         style = "lisrel",
         sizeLat = 10,
         sizeLat2 = 10,
         sizeMan = 6,
         edge.color = "steelblue",
         edge.label.cex = 2,
         label.cex = 2,
         rotation = 2,
         layout = "tree2",
         intercepts = TRUE,
         residuals = FALSE,
         #residScale = 10,
         curve = 2,
         title = T,
         title.color = "black",
         cardinal = "lat cov",
         curvePivot = T,
         nCharNodes = 6,
         #nodeLabels = label,
         mar = c(2,5,2,6))
# Title 
title("Multi-group CFA on MID task Contrasts")

3 Running [semi-restricted] ESEM Model

As described in the manuscript, the restricted CFA may incorrectly account for some measurement error in the items. This may degrade the fit statistics. See Marsh et al. (2014) for an in-depth discussion.

In this case, Exploratory Structural Equation Modeling (ESEM) is used to fit a CFA pre-specified model that allows for non-zero loadings. The technique and application of ESEM is available through the psych esem and esemcomp package. Here, the esemcomp package is used to fit a model using the steps described by Mateus Silvestrin here and by Guàrdia-Olmos et al.. The github code for esemcomp is available here. Below can be used to download the esemComp package – which worked with R version 4.2.1 on x86_64-apply-dawin17.0 during September 2022.

devtools::install_github("MateusPsi/esemComp", build_vignettes = TRUE)

3.1 Selected items for ESEM

First, select the items that are consistent with those in the CFA model

# ordering so can specify numerically
esem_data = brain_set[,c("AWin_v_Neut_L_NAcc_run1"  ,"AWin_v_Neut_L_NAcc_run2" ,
                         "BWin_v_Neut_L_NAcc_run1"  ,"BWin_v_Neut_L_NAcc_run2" ,
                         "BWin_v_BLose_L_NAcc_run1" ,"BWin_v_BLose_L_NAcc_run2",
                          "AWin_v_Neut_R_NAcc_run1" , "AWin_v_Neut_R_NAcc_run2",
                          "BWin_v_Neut_R_NAcc_run1" , "BWin_v_Neut_R_NAcc_run2",
                          "BWin_v_BLose_R_NAcc_run1", "BWin_v_BLose_R_NAcc_run2",
                         # insula values apprach 
                         "AWin_v_Neut_R_Insula_run1","AWin_v_Neut_R_Insula_run2", 
                         "BWin_v_Neut_R_Insula_run1","BWin_v_Neut_R_Insula_run2", 
                         # avoidance
                         "ALose_v_Neut_L_Insula_run1","ALose_v_Neut_L_Insula_run2",
                         "BLose_v_Neut_L_Insula_run1","BLose_v_Neut_L_Insula_run2",
                         "BLose_v_BWin_L_Insula_run1","BLose_v_BWin_L_Insula_run2",
                         "ALose_v_Neut_R_Insula_run1","ALose_v_Neut_R_Insula_run2",
                         "BLose_v_Neut_R_Insula_run1","BLose_v_Neut_R_Insula_run2",
                         "BLose_v_BWin_R_Insula_run1","BLose_v_BWin_R_Insula_run2",
                         "set")]

3.2 Specify EFA Model

As described in March et al. (2014), create a target rotation for items onto factors. In this case two factors are specified by the CFA model, so factor 1 and factor 2 are specified in make_target.

target_rot <- make_target(28,mainloadings = list(f1 = 1:16, f2 = 17:28))
esem.efa <- esem_efa(data = esem_data[,1:28], nfactors = 2,
                     target = target_rot, fm = "ml")
## Loading required namespace: GPArotation
esem.efa$loadings
## 
## Loadings:
##                            ML1    ML2   
## AWin_v_Neut_L_NAcc_run1     0.421       
## AWin_v_Neut_L_NAcc_run2     0.459       
## BWin_v_Neut_L_NAcc_run1     0.455       
## BWin_v_Neut_L_NAcc_run2     0.414       
## BWin_v_BLose_L_NAcc_run1    0.398       
## BWin_v_BLose_L_NAcc_run2    0.364       
## AWin_v_Neut_R_NAcc_run1     0.516       
## AWin_v_Neut_R_NAcc_run2     0.564  0.112
## BWin_v_Neut_R_NAcc_run1     0.391       
## BWin_v_Neut_R_NAcc_run2     0.419       
## BWin_v_BLose_R_NAcc_run1    0.450       
## BWin_v_BLose_R_NAcc_run2    0.461       
## AWin_v_Neut_R_Insula_run1   0.204       
## AWin_v_Neut_R_Insula_run2   0.226       
## BWin_v_Neut_R_Insula_run1   0.245       
## BWin_v_Neut_R_Insula_run2   0.255       
## ALose_v_Neut_L_Insula_run1         0.470
## ALose_v_Neut_L_Insula_run2         0.435
## BLose_v_Neut_L_Insula_run1         0.450
## BLose_v_Neut_L_Insula_run2         0.431
## BLose_v_BWin_L_Insula_run1         0.462
## BLose_v_BWin_L_Insula_run2         0.451
## ALose_v_Neut_R_Insula_run1         0.466
## ALose_v_Neut_R_Insula_run2         0.427
## BLose_v_Neut_R_Insula_run1         0.502
## BLose_v_Neut_R_Insula_run2         0.489
## BLose_v_BWin_R_Insula_run1         0.228
## BLose_v_BWin_R_Insula_run2         0.215
## 
##                  ML1   ML2
## SS loadings    2.616 2.243
## Proportion Var 0.093 0.080
## Cumulative Var 0.093 0.174

Using item that loads highest on factor 1 and lowest on factor 2 and vice versa, and define as anchor using find_referents

# per the example from Mateus Silverstrin, need to define anchor for each factor (value to loads highers on 1 factor and lowest on other)
anchor <- find_referents(efa_object = esem.efa,factor_names = c("f1","f2"))

Once the esem efa and anchors are defined, use syntax_composer to specied the esem model. This will produce a lavaan specified model that references starting values that will be used in the cfa model

# Pull starting parameters
esem_mid_model <- syntax_composer(efa_object = esem.efa, referents = anchor)

3.3 Run ESEM model

3.3.1 Specified Model

The starting values are printed below to provide reference for how starting values differ from a strict CFA model. Notice, how some values that were original not fit onto the Approach factor (f1), such as big lose contrasts, they are now specified with loading values that are between .05 to -.05.

cat(esem_mid_model)
## f1 =~ start(0.421)*AWin_v_Neut_L_NAcc_run1+
## start(0.459)*AWin_v_Neut_L_NAcc_run2+
## start(0.455)*BWin_v_Neut_L_NAcc_run1+
## start(0.414)*BWin_v_Neut_L_NAcc_run2+
## start(0.398)*BWin_v_BLose_L_NAcc_run1+
## start(0.364)*BWin_v_BLose_L_NAcc_run2+
## start(0.516)*AWin_v_Neut_R_NAcc_run1+
## start(0.564)*AWin_v_Neut_R_NAcc_run2+
## start(0.391)*BWin_v_Neut_R_NAcc_run1+
## start(0.419)*BWin_v_Neut_R_NAcc_run2+
## start(0.45)*BWin_v_BLose_R_NAcc_run1+
## start(0.461)*BWin_v_BLose_R_NAcc_run2+
## start(0.204)*AWin_v_Neut_R_Insula_run1+
## start(0.226)*AWin_v_Neut_R_Insula_run2+
## start(0.245)*BWin_v_Neut_R_Insula_run1+
## start(0.255)*BWin_v_Neut_R_Insula_run2+
## start(0.012)*ALose_v_Neut_L_Insula_run1+
## start(0.016)*ALose_v_Neut_L_Insula_run2+
## start(0.012)*BLose_v_Neut_L_Insula_run1+
## start(0.025)*BLose_v_Neut_L_Insula_run2+
## start(0.01)*BLose_v_BWin_L_Insula_run1+
## start(0)*BLose_v_BWin_L_Insula_run2+
## start(-0.019)*ALose_v_Neut_R_Insula_run1+
## start(-0.054)*ALose_v_Neut_R_Insula_run2+
## 0.004*BLose_v_Neut_R_Insula_run1+
## start(0.009)*BLose_v_Neut_R_Insula_run2+
## start(-0.058)*BLose_v_BWin_R_Insula_run1+
## start(-0.073)*BLose_v_BWin_R_Insula_run2 
## 
## f2 =~ start(-0.034)*AWin_v_Neut_L_NAcc_run1+
## start(-0.034)*AWin_v_Neut_L_NAcc_run2+
## start(-0.037)*BWin_v_Neut_L_NAcc_run1+
## start(0.019)*BWin_v_Neut_L_NAcc_run2+
## start(-0.063)*BWin_v_BLose_L_NAcc_run1+
## start(-0.084)*BWin_v_BLose_L_NAcc_run2+
## start(0.079)*AWin_v_Neut_R_NAcc_run1+
## 0.112*AWin_v_Neut_R_NAcc_run2+
## start(0.03)*BWin_v_Neut_R_NAcc_run1+
## start(0.011)*BWin_v_Neut_R_NAcc_run2+
## start(-0.029)*BWin_v_BLose_R_NAcc_run1+
## start(-0.02)*BWin_v_BLose_R_NAcc_run2+
## start(-0.03)*AWin_v_Neut_R_Insula_run1+
## start(-0.012)*AWin_v_Neut_R_Insula_run2+
## start(0.021)*BWin_v_Neut_R_Insula_run1+
## start(-0.026)*BWin_v_Neut_R_Insula_run2+
## start(0.47)*ALose_v_Neut_L_Insula_run1+
## start(0.435)*ALose_v_Neut_L_Insula_run2+
## start(0.45)*BLose_v_Neut_L_Insula_run1+
## start(0.431)*BLose_v_Neut_L_Insula_run2+
## start(0.462)*BLose_v_BWin_L_Insula_run1+
## start(0.451)*BLose_v_BWin_L_Insula_run2+
## start(0.466)*ALose_v_Neut_R_Insula_run1+
## start(0.427)*ALose_v_Neut_R_Insula_run2+
## start(0.502)*BLose_v_Neut_R_Insula_run1+
## start(0.489)*BLose_v_Neut_R_Insula_run2+
## start(0.228)*BLose_v_BWin_R_Insula_run1+
## start(0.215)*BLose_v_BWin_R_Insula_run2

3.3.2 Running full ESEM model

After the EFA loadings are extracted using a target rotation, starting values are now available. These are now used to specify a less restrictive CFA model

esem_mid_fit<- cfa(esem_mid_model, esem_data[,1:28], std.lv=TRUE, meanstructure = TRUE,
                   estimator = "MLR")

Pull and add fit statistics to the out dataframe and print results to see decreases in AIC/BIC

# adding values to the CFA model fit indices
out[4,2:8] <- round(data.matrix(fitmeasures(esem_mid_fit, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi","tli", "srmr"))), 
                    digits=3)
out[4,9] <- round(AIC(esem_mid_fit),3)
out[4,10] <- round(BIC(esem_mid_fit),3)
out[4,1] <-  c("Overall ESEM")

out <- as.data.frame(out)

out %>% 
  knitr::kable(
    col.names = c("Model", "Chi-sq", "DF", "p value", "RMSEA", "CFI", "TLI","SRMR", "AIC", "BIC"),
    caption = "Fit statistics from MG-CFA and ESEM models",
    booktabs = TRUE
    )
Fit statistics from MG-CFA and ESEM models
Model Chi-sq DF p value RMSEA CFI TLI SRMR AIC BIC
Overall CFA 2200.622 349 0 0.065 0.657 0.628 0.053 -21672.085 -21234.81
Configg MG-CFA 2961.409 1047 0 0.066 0.65 0.621 0.06 -21482.229 -20170.405
Metric MG-CFA 3024.264 1099 0 0.064 0.648 0.637 0.062 -21523.374 -20479.059
Overall ESEM 2174.511 323 0 0.067 0.657 0.598 0.052 -21646.197 -21075.167

4 Aim: 2. Running EFA [Unrestricted] model

Here, a data-driven exploratory factor analysis is performed as implemented using the (https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/factanal)[https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/factanal] in the stats package. The same variables as in the CFA and ESEM dataset are used. A tutorial from Nilam Ram on EFA is also available here

4.1 By Sample EFA

Used the (factanal)[https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/factanal] to run EFA model. Specifying the number of factors and using the promax (non-orthogonal) rotation.

abcd_efa_df <- esem_data %>% filter(set == 1)
mls_efa_df <- esem_data %>% filter(set == 2)
ahrb_efa_df <- esem_data %>% filter(set == 3)

4.1.1 Sample: ABCD

A number of methods can be used to estimate the recommended data driven factors in the data. There are nuanced differences in calculations between packages and methods. Therefore, a number of packages are used to acquire consistent evidence to acquire the most parsimonious model.

Using nFactors package see the recommended factors for the EFA model using a number of models.

fa_abcd <- subset(abcd_efa_df[,1:28])
plot(nScree(x=fa_abcd,model="factors"))

To avoid biasing of packages in different calculations of recommendation factors that depend on strong correlations between bilateral regions by using parallel analysis. Parallel analysis is also implemented using the paran package.

paran(x = fa_abcd,
      iterations = 1000, quietly = FALSE, centile = 95, 
      status = FALSE, all = TRUE, cfa = TRUE, graph = TRUE, color = TRUE, 
      col = c("black", "red", "blue"), lty = c(1, 2, 3), lwd = 1, legend = TRUE, 
      seed = 100)
## 
## Using eigendecomposition of correlation matrix.
## 
## Results of Horn's Parallel Analysis for factor retention
## 1000 iterations, using the 95 centile estimate
## 
## -------------------------------------------------- 
## Factor      Adjusted    Unadjusted    Estimated 
##             Eigenvalue  Eigenvalue    Bias 
## -------------------------------------------------- 
## No components passed. 
## -------------------------------------------------- 
## 1           3.542178    3.934015      0.391836
## 2           0.775202    1.111071      0.335869
## 3           0.313670    0.613506      0.299835
## 4           0.313864    0.580679      0.266815
## 5           0.271159    0.509467      0.238307
## 6           0.287997    0.500248      0.212250
## 7           0.272560    0.460549      0.187988
## 8           0.214122    0.380351      0.166228
## 9           0.218417    0.361595      0.143178
## 10          0.169955    0.291872      0.121916
## 11          0.141768    0.244225      0.102457
## 12          0.140901    0.223414      0.082512
## 13          0.148606    0.210788      0.062181
## 14          0.125450    0.168313      0.042863
## 15         -0.122634   -0.09868      0.023946
## 16         -0.129530   -0.12376      0.005761
## 17         -0.126362   -0.13831     -0.01194
## 18         -0.130790   -0.16166     -0.03087
## 19         -0.121125   -0.16974     -0.04861
## 20         -0.108212   -0.17507     -0.06685
## 21         -0.093136   -0.17720     -0.08406
## 22         -0.095347   -0.19714     -0.10179
## 23         -0.110512   -0.23053     -0.12002
## 24         -0.109017   -0.24716     -0.13814
## 25         -0.092890   -0.25014     -0.15725
## 26         -0.090723   -0.26576     -0.17504
## 27         -0.077950   -0.27668     -0.19873
## 28         -0.077263   -0.30109     -0.22383
## -------------------------------------------------- 
## 
## Adjusted eigenvalues > 0 indicate dimensions to retain.
## (14 factors    retained)

Comparing the above with the BIC comparison of an EFA model to determine the best fitting model based on fit statistics. Factor Analysis is submitted across a range of factors, e.g., 1-5, and the BIC is extracted from the model to determine the optimal number of factors

abcd_rec_factors <- matrix(NA, ncol = 2, nrow = 20)
colnames(abcd_rec_factors) <- c("Nfactors","BIC")

for (f in 1:20) {
  test_fac <- fa(r = fa_abcd,  #raw data  
            nfactors = f, fm = 'minres',
            rotate = "oblimin")
  abcd_rec_factors[f,1] <- f
  abcd_rec_factors[f,2] <-test_fac$BIC
}
## Warning in GPFoblq(L, Tmat = Tmat, normalize = normalize, eps = eps, maxit =
## maxit, : convergence not obtained in GPFoblq. 1000 iterations used.

## Warning in GPFoblq(L, Tmat = Tmat, normalize = normalize, eps = eps, maxit =
## maxit, : convergence not obtained in GPFoblq. 1000 iterations used.

## Warning in GPFoblq(L, Tmat = Tmat, normalize = normalize, eps = eps, maxit =
## maxit, : convergence not obtained in GPFoblq. 1000 iterations used.

## Warning in GPFoblq(L, Tmat = Tmat, normalize = normalize, eps = eps, maxit =
## maxit, : convergence not obtained in GPFoblq. 1000 iterations used.
abcd_bic_fact = as.data.frame(abcd_rec_factors)
abcd_lowest_bic <- which.min(abcd_bic_fact$BIC)

abcd_bic_fact %>% 
  ggplot(aes(x = Nfactors, y = BIC)) +
  geom_line(colour = 'black', linetype = 'dashed') +
  geom_vline(xintercept = abcd_bic_fact$Nfactors[abcd_lowest_bic], colour = 'red')+
  theme_minimal()

Running EFA

abcd_efa <- factanal(x = fa_abcd,  #raw data  
              factors = 2, fm ='minres', rotation = "promax" # oblique rotation allow for non-orthogonal structure
              )
heatmaply(round(abcd_efa$loadings[,1:2],2) %>% print(sort = T),
          scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
                 low = "blue", 
                 high = "darkred", 
                 space = "Lab",
                 midpoint = 0, 
                 limits = c(-1, 1)
               ),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 9, fontsize_col = 9,
               labCol = colnames(abcd_efa$loadings[,1:2]),
               labRow = rownames(abcd_efa$loadings[,1:2]),
               heatmap_layers = theme(axis.line=element_blank()),
          
)
##                            Factor1 Factor2
## AWin_v_Neut_L_NAcc_run1       0.40   -0.06
## AWin_v_Neut_L_NAcc_run2       0.45   -0.04
## BWin_v_Neut_L_NAcc_run1       0.47   -0.04
## BWin_v_Neut_L_NAcc_run2       0.41   -0.01
## BWin_v_BLose_L_NAcc_run1      0.42   -0.07
## BWin_v_BLose_L_NAcc_run2      0.37   -0.07
## AWin_v_Neut_R_NAcc_run1       0.54    0.12
## AWin_v_Neut_R_NAcc_run2       0.61    0.14
## BWin_v_Neut_R_NAcc_run1       0.39    0.01
## BWin_v_Neut_R_NAcc_run2       0.41   -0.01
## BWin_v_BLose_R_NAcc_run1      0.44   -0.04
## BWin_v_BLose_R_NAcc_run2      0.49    0.00
## AWin_v_Neut_R_Insula_run1     0.21   -0.04
## AWin_v_Neut_R_Insula_run2     0.25   -0.03
## BWin_v_Neut_R_Insula_run1     0.23   -0.01
## BWin_v_Neut_R_Insula_run2     0.22   -0.08
## ALose_v_Neut_L_Insula_run1    0.03    0.46
## ALose_v_Neut_L_Insula_run2    0.03    0.42
## BLose_v_Neut_L_Insula_run1    0.05    0.48
## BLose_v_Neut_L_Insula_run2    0.05    0.46
## BLose_v_BWin_L_Insula_run1    0.03    0.46
## BLose_v_BWin_L_Insula_run2    0.02    0.43
## ALose_v_Neut_R_Insula_run1    0.00    0.50
## ALose_v_Neut_R_Insula_run2   -0.01    0.44
## BLose_v_Neut_R_Insula_run1    0.02    0.51
## BLose_v_Neut_R_Insula_run2    0.04    0.50
## BLose_v_BWin_R_Insula_run1   -0.06    0.18
## BLose_v_BWin_R_Insula_run2   -0.06    0.18
## Warning: `gather_()` was deprecated in tidyr 1.2.0.
## ℹ Please use `gather()` instead.
## ℹ The deprecated feature was likely used in the plotly package.
##   Please report the issue at <https://github.com/plotly/plotly.R/issues>.

4.1.2 Sample: MLS

fa_mls <- subset(mls_efa_df[,1:28])
plot(nScree(x=fa_mls,model="factors"))

paran(x = fa_mls,
      iterations = 1000, quietly = FALSE, centile = 95, 
      status = FALSE, all = TRUE, cfa = TRUE, graph = TRUE, color = TRUE, 
      col = c("black", "red", "blue"), lty = c(1, 2, 3), lwd = 1, legend = TRUE, 
      seed = 100)
## 
## Using eigendecomposition of correlation matrix.
## 
## Results of Horn's Parallel Analysis for factor retention
## 1000 iterations, using the 95 centile estimate
## 
## -------------------------------------------------- 
## Factor      Adjusted    Unadjusted    Estimated 
##             Eigenvalue  Eigenvalue    Bias 
## -------------------------------------------------- 
## 1           2.831197    4.041832      1.210634
## 2           0.383345    1.415416      1.032070
## 3           0.170152    1.081438      0.911286
## 4           0.169402    0.976468      0.807066
## 5           0.161286    0.886233      0.724946
## 6           0.110471    0.757309      0.646837
## 7           0.051888    0.631413      0.579524
## 8           0.072342    0.588307      0.515965
## 9           0.009946    0.458769      0.448823
## 10          0.032104    0.421235      0.389130
## 11          0.032538    0.363316      0.330777
## 12         -0.042810    0.232814      0.275625
## 13         -0.013344    0.211961      0.225305
## 14          0.014754    0.191760      0.177006
## 15         -0.039773    0.090890      0.130663
## 16         -0.049639    0.036074      0.085713
## 17         -0.040487   -0.00265      0.037831
## 18         -0.066096   -0.07167     -0.00558
## 19         -0.084986   -0.13281     -0.04782
## 20         -0.056403   -0.14665     -0.09025
## 21         -0.037420   -0.16846     -0.13104
## 22         -0.014872   -0.18121     -0.16634
## 23          0.011672   -0.19418     -0.20586
## 24          0.011884   -0.23185     -0.24374
## 25         -0.019505   -0.29958     -0.28007
## 26          0.010809   -0.30709     -0.31790
## 27          0.003662   -0.35286     -0.35652
## 28          0.008372   -0.39046     -0.39884
## -------------------------------------------------- 
## 
## Adjusted eigenvalues > 0 indicate dimensions to retain.
## (11 factors    retained)

mls_rec_factors <- matrix(NA, ncol = 2, nrow = 10)
colnames(mls_rec_factors) <- c("Nfactors","BIC")

for (f in 1:10) {
  test_fac <- fa(r = fa_mls,  #raw data  
            nfactors = f, fm = 'minres',
            rotate = "promax")
  mls_rec_factors[f,1] <- f
  mls_rec_factors[f,2] <-test_fac$BIC
}

mls_bic_fact = as.data.frame(mls_rec_factors)
mls_lowest_bic <- which.min(mls_bic_fact$BIC)

mls_bic_fact %>% 
  ggplot(aes(x = Nfactors, y = BIC)) +
  geom_line(colour = 'black', linetype = 'dashed') +
  geom_vline(xintercept = mls_bic_fact$Nfactors[mls_lowest_bic], colour = 'red')+
  theme_minimal()

MLS factor analysis

mls_efa <- factanal(x = fa_mls,  #raw data  
              factors = 3, rotation = "promax" # oblique rotation allow for non-orthogonal structure
              )
heatmaply(round(mls_efa$loadings[,1:3],2) %>% print(sort = T),
          scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
                 low = "blue", 
                 high = "darkred", 
                 space = "Lab",
                 midpoint = 0, 
                 limits = c(-1, 1)
               ),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 9, fontsize_col = 9,
               labCol = colnames(mls_efa$loadings[,1:3]),
               labRow = rownames(mls_efa$loadings[,1:3]),
               heatmap_layers = theme(axis.line=element_blank()),
          
)
##                            Factor1 Factor2 Factor3
## AWin_v_Neut_L_NAcc_run1       0.55    0.25   -0.02
## AWin_v_Neut_L_NAcc_run2       0.51    0.06   -0.03
## BWin_v_Neut_L_NAcc_run1       0.42    0.04   -0.01
## BWin_v_Neut_L_NAcc_run2       0.33    0.07    0.00
## BWin_v_BLose_L_NAcc_run1      0.32   -0.06    0.07
## BWin_v_BLose_L_NAcc_run2      0.27   -0.12   -0.10
## AWin_v_Neut_R_NAcc_run1       0.68   -0.05    0.30
## AWin_v_Neut_R_NAcc_run2       0.51   -0.19    0.42
## BWin_v_Neut_R_NAcc_run1       0.42    0.19   -0.05
## BWin_v_Neut_R_NAcc_run2       0.29    0.00   -0.04
## BWin_v_BLose_R_NAcc_run1      0.53    0.15   -0.20
## BWin_v_BLose_R_NAcc_run2      0.28    0.02   -0.24
## AWin_v_Neut_R_Insula_run1     0.13   -0.13    0.12
## AWin_v_Neut_R_Insula_run2     0.01   -0.13    0.22
## BWin_v_Neut_R_Insula_run1     0.30   -0.02    0.22
## BWin_v_Neut_R_Insula_run2     0.30   -0.04    0.15
## ALose_v_Neut_L_Insula_run1   -0.01    0.42    0.13
## ALose_v_Neut_L_Insula_run2    0.04    0.30    0.18
## BLose_v_Neut_L_Insula_run1    0.03    0.05    0.56
## BLose_v_Neut_L_Insula_run2    0.06    0.16    0.54
## BLose_v_BWin_L_Insula_run1    0.16    0.87   -0.11
## BLose_v_BWin_L_Insula_run2    0.02    0.65    0.05
## ALose_v_Neut_R_Insula_run1    0.14    0.42    0.09
## ALose_v_Neut_R_Insula_run2   -0.09    0.46    0.00
## BLose_v_Neut_R_Insula_run1   -0.11    0.23    0.28
## BLose_v_Neut_R_Insula_run2   -0.16    0.17    0.29
## BLose_v_BWin_R_Insula_run1   -0.07    0.38    0.05
## BLose_v_BWin_R_Insula_run2   -0.23    0.35   -0.12

4.1.3 Sample: AHRB

fa_ahrb <- subset(ahrb_efa_df[,1:28])
plot(nScree(x=fa_ahrb,model="factors"))

paran(x = fa_ahrb,
      iterations = 1000, quietly = FALSE, centile = 95, 
      status = FALSE, all = TRUE, cfa = TRUE, graph = TRUE, color = TRUE, 
      col = c("black", "red", "blue"), lty = c(1, 2, 3), lwd = 1, legend = TRUE, 
      seed = 100)
## 
## Using eigendecomposition of correlation matrix.
## 
## Results of Horn's Parallel Analysis for factor retention
## 1000 iterations, using the 95 centile estimate
## 
## -------------------------------------------------- 
## Factor      Adjusted    Unadjusted    Estimated 
##             Eigenvalue  Eigenvalue    Bias 
## -------------------------------------------------- 
## 1           2.060093    3.621941      1.561847
## 2           0.481724    1.810384      1.328660
## 3           0.076629    1.242826      1.166197
## 4           0.189243    1.228597      1.039354
## 5          -0.009360    0.929113      0.938474
## 6          -0.050147    0.785260      0.835407
## 7           0.030826    0.765686      0.734860
## 8           0.030113    0.684464      0.654351
## 9           0.068039    0.646615      0.578576
## 10          0.031492    0.535404      0.503911
## 11         -0.050998    0.383378      0.434377
## 12         -0.061551    0.305570      0.367122
## 13         -0.045811    0.260598      0.306410
## 14         -0.087183    0.158940      0.246124
## 15         -0.048996    0.140764      0.189761
## 16         -0.047886    0.083183      0.131069
## 17         -0.083831   -0.00786      0.075962
## 18         -0.090172   -0.06397      0.026192
## 19         -0.083539   -0.10575     -0.02221
## 20         -0.034889   -0.10723     -0.07234
## 21         -0.004630   -0.12541     -0.12078
## 22          0.002853   -0.16359     -0.16644
## 23         -0.014767   -0.22211     -0.20734
## 24          0.009603   -0.23872     -0.24833
## 25         -0.014051   -0.30408     -0.29003
## 26          0.012237   -0.31880     -0.33104
## 27          0.033983   -0.33629     -0.37027
## 28          0.028916   -0.37918     -0.40809
## -------------------------------------------------- 
## 
## Adjusted eigenvalues > 0 indicate dimensions to retain.
## (4 factors    retained)

ahrb_rec_factors <- matrix(NA, ncol = 2, nrow = 10)
colnames(ahrb_rec_factors) <- c("Nfactors","BIC")

for (f in 1:10) {
  test_fac <- fa(r = fa_ahrb,  #raw data  
            nfactors = f, fm = 'minres',
            rotate = "promax")
  ahrb_rec_factors[f,1] <- f
  ahrb_rec_factors[f,2] <-test_fac$BIC
}

ahrb_bic_fact = as.data.frame(ahrb_rec_factors)
ahrb_lowest_bic <- which.min(ahrb_bic_fact$BIC)

ahrb_bic_fact %>% 
  ggplot(aes(x = Nfactors, y = BIC)) +
  geom_line(colour = 'black', linetype = 'dashed') +
  geom_vline(xintercept = ahrb_bic_fact$Nfactors[ahrb_lowest_bic], colour = 'red')+
  theme_minimal()

Factor Analysis Model

ahrb_efa <- factanal(x = fa_ahrb,  #raw data  
              factors = 4, rotation = "promax" # oblique rotation allow for non-orthogonal structure
              )
heatmaply(round(ahrb_efa$loadings[,1:4],2) %>% print(sort = T),
          scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
                 low = "blue", 
                 high = "darkred", 
                 space = "Lab",
                 midpoint = 0, 
                 limits = c(-1, 1)
               ),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 9, fontsize_col = 9,
               labCol = colnames(ahrb_efa$loadings[,1:4]),
               labRow = rownames(ahrb_efa$loadings[,1:4]),
               heatmap_layers = theme(axis.line=element_blank()),
          
)
##                            Factor1 Factor2 Factor3 Factor4
## AWin_v_Neut_L_NAcc_run1      -0.24    0.51   -0.09   -0.04
## AWin_v_Neut_L_NAcc_run2       0.03    0.72   -0.12   -0.11
## BWin_v_Neut_L_NAcc_run1      -0.01    0.19    0.13   -0.21
## BWin_v_Neut_L_NAcc_run2      -0.09    0.39   -0.11    0.14
## BWin_v_BLose_L_NAcc_run1     -0.39    0.00    0.11    0.22
## BWin_v_BLose_L_NAcc_run2     -0.13    0.02    0.44    0.05
## AWin_v_Neut_R_NAcc_run1      -0.40    0.27    0.03    0.12
## AWin_v_Neut_R_NAcc_run2      -0.23    0.10    0.21    0.23
## BWin_v_Neut_R_NAcc_run1       0.20   -0.25    0.93   -0.14
## BWin_v_Neut_R_NAcc_run2       0.25    0.26    0.59   -0.05
## BWin_v_BLose_R_NAcc_run1     -0.08    0.38    0.08    0.13
## BWin_v_BLose_R_NAcc_run2     -0.13    0.22    0.29   -0.09
## AWin_v_Neut_R_Insula_run1    -0.07    0.21   -0.06    0.09
## AWin_v_Neut_R_Insula_run2     0.26    0.23    0.22   -0.11
## BWin_v_Neut_R_Insula_run1     0.21    0.49   -0.22   -0.15
## BWin_v_Neut_R_Insula_run2     0.17    0.39    0.04    0.04
## ALose_v_Neut_L_Insula_run1    0.51    0.16   -0.10    0.19
## ALose_v_Neut_L_Insula_run2    0.46    0.15   -0.14    0.24
## BLose_v_Neut_L_Insula_run1    0.51   -0.12    0.13    0.09
## BLose_v_Neut_L_Insula_run2    0.30    0.02    0.13    0.03
## BLose_v_BWin_L_Insula_run1   -0.02   -0.17   -0.04    0.49
## BLose_v_BWin_L_Insula_run2    0.09   -0.13   -0.05    0.49
## ALose_v_Neut_R_Insula_run1    0.66   -0.01    0.24    0.09
## ALose_v_Neut_R_Insula_run2    0.47   -0.23    0.18    0.19
## BLose_v_Neut_R_Insula_run1    0.18    0.01    0.03    0.49
## BLose_v_Neut_R_Insula_run2    0.15    0.04   -0.17    0.55
## BLose_v_BWin_R_Insula_run1    0.21   -0.13   -0.02    0.19
## BLose_v_BWin_R_Insula_run2    0.23    0.03   -0.07    0.25

4.2 Quant. Convergence

Calculating a coefficient of factor congruence across the three sample’s EFA models. Using function fa.congruence

fa.congruence(x = list(abcd_efa, mls_efa, ahrb_efa), digits = 2) %>% 
  knitr::kable(
    col.names = c("1. ABCD F1", "2. ABCD F2", 
                  "3. MLS F1", "4. MLS F2","5. MLS F3",
                  "6. AHRB F1", "7. AHRB F2","8. AHRB F3", "8. AHRB F4"),
    caption = "ABCD, MLS and AHRB EFA Factor Congruence",
    booktabs = TRUE
    )
ABCD, MLS and AHRB EFA Factor Congruence
1. ABCD F1 2. ABCD F2 3. MLS F1 4. MLS F2 5. MLS F3 6. AHRB F1 7. AHRB F2 8. AHRB F3 8. AHRB F4
Factor1 1.00 0.03 0.94 0.03 0.20 -0.17 0.68 0.47 0.07
Factor2 0.03 1.00 -0.02 0.76 0.58 0.68 -0.11 0.04 0.77
Factor1 0.94 -0.02 1.00 0.07 0.15 -0.21 0.68 0.38 -0.01
Factor2 0.03 0.76 0.07 1.00 0.05 0.51 -0.07 0.02 0.67
Factor3 0.20 0.58 0.15 0.05 1.00 0.37 0.13 0.00 0.34
Factor1 -0.17 0.68 -0.21 0.51 0.37 1.00 -0.06 0.17 0.22
Factor2 0.68 -0.11 0.68 -0.07 0.13 -0.06 1.00 -0.12 -0.09
Factor3 0.47 0.04 0.38 0.02 0.00 0.17 -0.12 1.00 -0.13
Factor4 0.07 0.77 -0.01 0.67 0.34 0.22 -0.09 -0.13 1.00

5 Running Local SEM

Running CFA for the pubertal variables in the ABCD sample using the local SEM framework described in Olaru et al (2020) implemented using the sirt package

5.1 Run LSEM

Specifying the model for the ABCD data below. For now, using the CFA model. In future [real data] implementation, will apply the EFA CFA from n = 1000 ABCD sample in the held out n = 1000 ABCD sample. Piloting on the simulated PDS scale

#first adding random PDS variable
set.seed(110)
sim_ABCD_data$PDS <- as.integer(rtnorm(n=1000, mean = 3.5, sd = 1.5, 
                                       lower = 1, upper = 7))

lsem.MID <- sirt::lsem.estimate(data = sim_ABCD_data, moderator = 'PDS', # moderator variable
                                moderator.grid = seq(1,5,1), # moderator levels, PDS 1 - 5
                                lavmodel = MID_model, # model
                                h = 2, # bandwidth parameter 
                                residualize = FALSE, # allow mean level differences 
                                meanstructure = TRUE,
                                std.lv=TRUE
                                )
## ** Fit lavaan model
## |*****|
## |-----|
## ** Parameter summary

5.2 Summary LSEM

Summarizing output of the lsem.estimate

summary(lsem.MID)
## -----------------------------------------------------------------
## Local Structural Equation Model 
## 
## sirt 3.12-66 (2022-05-16 12:27:54) 
## lavaan 0.6-12 (2022-07-04 16:40:02 UTC) 
## 
## R version 4.2.1 (2022-06-23) x86_64, darwin17.0 | nodename=Michaels-MacBook-Pro.local | login=root 
## 
## Function 'sirt::lsem.estimate', type='LSEM' 
## 
## 
## Call:
## sirt::lsem.estimate(data = sim_ABCD_data, moderator = "PDS", 
##     moderator.grid = seq(1, 5, 1), lavmodel = MID_model, h = 2, 
##     residualize = FALSE, meanstructure = TRUE, std.lv = TRUE)
## 
## Date of Analysis: 2022-11-11 11:26:51 
## Time difference of 5.015015 secs
## Computation Time: 5.015015 
## 
## Number of observations in datasets = 1000 
## Used observations in analysis = 1000 
## Used sampling weights: FALSE 
## Bandwidth factor = 2 
## Bandwidth = 0.648 
## Number of focal points for moderator = 5 
## 
## Used joint estimation: FALSE 
## Used sufficient statistics: FALSE 
## Used local linear smoothing: FALSE 
## Used pseudo weights: FALSE 
## Used lavaan package: TRUE 
## Used lavaan.survey package: FALSE 
## 
## Mean structure modelled: TRUE 
## 
## lavaan Model
## 
## 
## # Factor loadings
## Approach =~ AWin_v_Neut_L_NAcc_run1  + AWin_v_Neut_R_NAcc_run1  + AWin_v_Neut_R_Insula_run1 +
##             AWin_v_Neut_L_NAcc_run2  + AWin_v_Neut_R_NAcc_run2 + AWin_v_Neut_R_Insula_run2 +
##             BWin_v_Neut_L_NAcc_run1  + BWin_v_Neut_R_NAcc_run1  + BWin_v_Neut_R_Insula_run1 +
##             BWin_v_Neut_L_NAcc_run2  + BWin_v_Neut_R_NAcc_run2  + BWin_v_Neut_R_Insula_run2 +
##             BWin_v_BLose_L_NAcc_run1 + BWin_v_BLose_R_NAcc_run1 +
##             BWin_v_BLose_L_NAcc_run2 + BWin_v_BLose_R_NAcc_run2 
##                 
## Avoid =~    ALose_v_Neut_L_Insula_run1 + ALose_v_Neut_R_Insula_run1 +
##             ALose_v_Neut_L_Insula_run2 + ALose_v_Neut_R_Insula_run2 +
##             BLose_v_Neut_L_Insula_run1 + BLose_v_Neut_R_Insula_run1 +
##             BLose_v_Neut_L_Insula_run2 + BLose_v_Neut_R_Insula_run2 +
##             BLose_v_BWin_L_Insula_run1 + BLose_v_BWin_R_Insula_run1 +
##             BLose_v_BWin_L_Insula_run2 + BLose_v_BWin_R_Insula_run2 
## 
## 
## Parameter Estimate Summary
## 
##                                                       par parindex      M    SD
## 1                       Approach=~AWin_v_Neut_L_NAcc_run1        1  0.082 0.006
## 2                       Approach=~AWin_v_Neut_R_NAcc_run1        2  0.086 0.004
## 3                     Approach=~AWin_v_Neut_R_Insula_run1        3  0.041 0.004
## 4                       Approach=~AWin_v_Neut_L_NAcc_run2        4  0.090 0.002
## 5                       Approach=~AWin_v_Neut_R_NAcc_run2        5  0.096 0.006
## 6                     Approach=~AWin_v_Neut_R_Insula_run2        6  0.049 0.007
## 7                       Approach=~BWin_v_Neut_L_NAcc_run1        7  0.095 0.009
## 8                       Approach=~BWin_v_Neut_R_NAcc_run1        8  0.070 0.007
## 9                     Approach=~BWin_v_Neut_R_Insula_run1        9  0.044 0.005
## 10                      Approach=~BWin_v_Neut_L_NAcc_run2       10  0.083 0.007
## 11                      Approach=~BWin_v_Neut_R_NAcc_run2       11  0.079 0.015
## 12                    Approach=~BWin_v_Neut_R_Insula_run2       12  0.050 0.011
## 13                     Approach=~BWin_v_BLose_L_NAcc_run1       13  0.092 0.006
## 14                     Approach=~BWin_v_BLose_R_NAcc_run1       14  0.089 0.005
## 15                     Approach=~BWin_v_BLose_L_NAcc_run2       15  0.079 0.008
## 16                     Approach=~BWin_v_BLose_R_NAcc_run2       16  0.095 0.004
## 17                      Avoid=~ALose_v_Neut_L_Insula_run1       17  0.087 0.003
## 18                      Avoid=~ALose_v_Neut_R_Insula_run1       18  0.094 0.009
## 19                      Avoid=~ALose_v_Neut_L_Insula_run2       19  0.078 0.008
## 20                      Avoid=~ALose_v_Neut_R_Insula_run2       20  0.090 0.012
## 21                      Avoid=~BLose_v_Neut_L_Insula_run1       21  0.086 0.013
## 22                      Avoid=~BLose_v_Neut_R_Insula_run1       22  0.092 0.006
## 23                      Avoid=~BLose_v_Neut_L_Insula_run2       23  0.082 0.006
## 24                      Avoid=~BLose_v_Neut_R_Insula_run2       24  0.091 0.005
## 25                      Avoid=~BLose_v_BWin_L_Insula_run1       25  0.085 0.016
## 26                      Avoid=~BLose_v_BWin_R_Insula_run1       26  0.040 0.010
## 27                      Avoid=~BLose_v_BWin_L_Insula_run2       27  0.077 0.014
## 28                      Avoid=~BLose_v_BWin_R_Insula_run2       28  0.041 0.004
## 29       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       29  0.028 0.001
## 30       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       30  0.031 0.002
## 31   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       31  0.029 0.002
## 32       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       32  0.027 0.001
## 33       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       33  0.028 0.002
## 34   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       34  0.028 0.002
## 35       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       35  0.025 0.001
## 36       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       36  0.029 0.001
## 37   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       37  0.031 0.001
## 38       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       38  0.030 0.001
## 39       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       39  0.030 0.002
## 40   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       40  0.031 0.001
## 41     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       41  0.028 0.002
## 42     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       42  0.030 0.003
## 43     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       43  0.028 0.001
## 44     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       44  0.028 0.002
## 45 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       45  0.030 0.002
## 46 ALose_v_Neut_R_Insula_run1~~ALose_v_Neut_R_Insula_run1       46  0.027 0.002
## 47 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       47  0.029 0.001
## 48 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       48  0.029 0.003
## 49 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       49  0.029 0.001
## 50 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       50  0.025 0.001
## 51 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51  0.030 0.002
## 52 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52  0.029 0.002
## 53 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       53  0.030 0.002
## 54 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       54  0.031 0.002
## 55 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       55  0.029 0.002
## 56 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       56  0.029 0.001
## 57                                     Approach~~Approach       57  1.000 0.000
## 58                                           Avoid~~Avoid       58  1.000 0.000
## 59                                        Approach~~Avoid       59 -0.577 0.037
## 60                              AWin_v_Neut_L_NAcc_run1~1       60 -0.003 0.016
## 61                              AWin_v_Neut_R_NAcc_run1~1       61 -0.004 0.009
## 62                            AWin_v_Neut_R_Insula_run1~1       62  0.007 0.004
## 63                              AWin_v_Neut_L_NAcc_run2~1       63 -0.002 0.009
## 64                              AWin_v_Neut_R_NAcc_run2~1       64  0.003 0.007
## 65                            AWin_v_Neut_R_Insula_run2~1       65  0.005 0.003
## 66                              BWin_v_Neut_L_NAcc_run1~1       66 -0.011 0.003
## 67                              BWin_v_Neut_R_NAcc_run1~1       67 -0.006 0.008
## 68                            BWin_v_Neut_R_Insula_run1~1       68  0.013 0.004
## 69                              BWin_v_Neut_L_NAcc_run2~1       69 -0.005 0.003
## 70                              BWin_v_Neut_R_NAcc_run2~1       70 -0.001 0.007
## 71                            BWin_v_Neut_R_Insula_run2~1       71 -0.001 0.006
## 72                             BWin_v_BLose_L_NAcc_run1~1       72 -0.003 0.009
## 73                             BWin_v_BLose_R_NAcc_run1~1       73 -0.005 0.011
## 74                             BWin_v_BLose_L_NAcc_run2~1       74 -0.008 0.010
## 75                             BWin_v_BLose_R_NAcc_run2~1       75 -0.008 0.008
## 76                           ALose_v_Neut_L_Insula_run1~1       76 -0.005 0.004
## 77                           ALose_v_Neut_R_Insula_run1~1       77  0.003 0.005
## 78                           ALose_v_Neut_L_Insula_run2~1       78 -0.001 0.005
## 79                           ALose_v_Neut_R_Insula_run2~1       79  0.002 0.005
## 80                           BLose_v_Neut_L_Insula_run1~1       80  0.002 0.009
## 81                           BLose_v_Neut_R_Insula_run1~1       81  0.014 0.008
## 82                           BLose_v_Neut_L_Insula_run2~1       82  0.013 0.003
## 83                           BLose_v_Neut_R_Insula_run2~1       83  0.005 0.006
## 84                           BLose_v_BWin_L_Insula_run1~1       84  0.008 0.006
## 85                           BLose_v_BWin_R_Insula_run1~1       85  0.002 0.005
## 86                           BLose_v_BWin_L_Insula_run2~1       86  0.005 0.004
## 87                           BLose_v_BWin_R_Insula_run2~1       87 -0.003 0.012
## 88                                             Approach~1       88  0.000 0.000
## 89                                                Avoid~1       89  0.000 0.000
## 90                                                  rmsea       90  0.075 0.005
## 91                                                    cfi       91  0.598 0.039
## 92                                                    tli       92  0.564 0.042
## 93                                                    gfi       93  0.860 0.014
## 94                                                   srmr       94  0.061 0.004
##      MAD    Min    Max lin_int lin_slo SD_nonlin
## 1  0.006  0.074  0.090   0.092  -0.003     0.005
## 2  0.003  0.081  0.092   0.087   0.000     0.003
## 3  0.003  0.036  0.047   0.043  -0.001     0.003
## 4  0.002  0.085  0.093   0.095  -0.002     0.001
## 5  0.003  0.086  0.109   0.107  -0.004     0.004
## 6  0.006  0.039  0.061   0.033   0.005     0.003
## 7  0.005  0.071  0.105   0.115  -0.007     0.004
## 8  0.006  0.063  0.080   0.060   0.003     0.005
## 9  0.003  0.034  0.055   0.056  -0.004     0.003
## 10 0.005  0.069  0.090   0.080   0.001     0.006
## 11 0.012  0.056  0.100   0.042   0.013     0.002
## 12 0.009  0.037  0.072   0.074  -0.008     0.006
## 13 0.005  0.076  0.097   0.101  -0.003     0.005
## 14 0.004  0.083  0.099   0.082   0.002     0.004
## 15 0.005  0.061  0.086   0.070   0.003     0.007
## 16 0.003  0.086  0.099   0.100  -0.002     0.003
## 17 0.002  0.082  0.092   0.088   0.000     0.003
## 18 0.008  0.080  0.105   0.072   0.007     0.003
## 19 0.007  0.068  0.088   0.096  -0.006     0.003
## 20 0.009  0.068  0.104   0.079   0.004     0.011
## 21 0.012  0.058  0.097   0.067   0.006     0.011
## 22 0.005  0.083  0.099   0.103  -0.004     0.004
## 23 0.005  0.070  0.088   0.073   0.003     0.005
## 24 0.004  0.081  0.095   0.089   0.001     0.005
## 25 0.015  0.062  0.104   0.048   0.013     0.007
## 26 0.009  0.028  0.056   0.057  -0.006     0.008
## 27 0.012  0.057  0.097   0.044   0.011     0.006
## 28 0.004  0.037  0.050   0.049  -0.003     0.003
## 29 0.001  0.026  0.029   0.027   0.000     0.001
## 30 0.002  0.028  0.033   0.026   0.002     0.001
## 31 0.002  0.026  0.032   0.029   0.000     0.002
## 32 0.001  0.025  0.027   0.026   0.000     0.001
## 33 0.001  0.027  0.033   0.025   0.001     0.001
## 34 0.002  0.025  0.032   0.034  -0.002     0.001
## 35 0.001  0.023  0.028   0.022   0.001     0.001
## 36 0.001  0.027  0.030   0.029   0.000     0.001
## 37 0.001  0.029  0.032   0.033  -0.001     0.001
## 38 0.001  0.028  0.032   0.033  -0.001     0.001
## 39 0.001  0.024  0.032   0.032  -0.001     0.002
## 40 0.001  0.029  0.033   0.031   0.000     0.001
## 41 0.001  0.025  0.033   0.032  -0.001     0.001
## 42 0.002  0.021  0.032   0.035  -0.002     0.002
## 43 0.001  0.027  0.029   0.030  -0.001     0.001
## 44 0.002  0.024  0.029   0.023   0.002     0.001
## 45 0.002  0.026  0.032   0.032  -0.001     0.002
## 46 0.002  0.024  0.030   0.032  -0.002     0.001
## 47 0.001  0.028  0.032   0.028   0.000     0.001
## 48 0.003  0.026  0.036   0.036  -0.002     0.002
## 49 0.001  0.025  0.029   0.031  -0.001     0.001
## 50 0.001  0.024  0.026   0.026   0.000     0.001
## 51 0.002  0.027  0.033   0.031   0.000     0.002
## 52 0.001  0.026  0.031   0.024   0.002     0.000
## 53 0.002  0.027  0.031   0.032  -0.001     0.002
## 54 0.002  0.028  0.035   0.036  -0.002     0.001
## 55 0.001  0.025  0.031   0.032  -0.001     0.001
## 56 0.001  0.028  0.030   0.030   0.000     0.001
## 57 0.000  1.000  1.000   1.000   0.000     0.000
## 58 0.000  1.000  1.000   1.000   0.000     0.000
## 59 0.033 -0.621 -0.517  -0.517  -0.020     0.028
## 60 0.014 -0.017  0.028   0.034  -0.013     0.006
## 61 0.008 -0.020  0.007   0.003  -0.002     0.008
## 62 0.003 -0.001  0.010   0.005   0.001     0.004
## 63 0.007 -0.012  0.013   0.018  -0.007     0.002
## 64 0.005 -0.011  0.011   0.016  -0.004     0.004
## 65 0.003  0.001  0.009   0.010  -0.002     0.003
## 66 0.003 -0.014 -0.005  -0.013   0.001     0.003
## 67 0.006 -0.011  0.014   0.007  -0.004     0.006
## 68 0.003  0.008  0.017   0.008   0.002     0.003
## 69 0.003 -0.009  0.000  -0.007   0.001     0.003
## 70 0.005 -0.006  0.018   0.010  -0.004     0.006
## 71 0.004 -0.010  0.015   0.011  -0.004     0.004
## 72 0.007 -0.010  0.016   0.005  -0.003     0.008
## 73 0.010 -0.019  0.010   0.018  -0.008     0.007
## 74 0.010 -0.017  0.011   0.007  -0.005     0.008
## 75 0.008 -0.017  0.005   0.003  -0.004     0.007
## 76 0.004 -0.009  0.003  -0.008   0.001     0.004
## 77 0.004 -0.008  0.009   0.015  -0.004     0.001
## 78 0.004 -0.008  0.007  -0.005   0.001     0.005
## 79 0.003 -0.010  0.007   0.009  -0.002     0.004
## 80 0.007 -0.006  0.024   0.012  -0.003     0.008
## 81 0.007  0.003  0.025  -0.006   0.007     0.003
## 82 0.003  0.009  0.016   0.011   0.001     0.003
## 83 0.006 -0.003  0.011  -0.002   0.002     0.005
## 84 0.005  0.001  0.016   0.018  -0.003     0.004
## 85 0.003 -0.011  0.006   0.008  -0.002     0.004
## 86 0.003 -0.002  0.009   0.007  -0.001     0.004
## 87 0.010 -0.030  0.005  -0.028   0.008     0.007
## 88 0.000  0.000  0.000   0.000   0.000     0.000
## 89 0.000  0.000  0.000   0.000   0.000     0.000
## 90 0.005  0.071  0.086   0.071   0.001     0.005
## 91 0.030  0.527  0.635   0.594   0.001     0.038
## 92 0.033  0.488  0.605   0.560   0.001     0.042
## 93 0.013  0.830  0.872   0.872  -0.004     0.013
## 94 0.003  0.058  0.069   0.060   0.000     0.004
## 
## Distribution of Moderator: Density and Effective Sample Size
## 
## M=3.083 | SD=1.289
## 
##   moderator   wgt    Neff
## 1         1 0.125 188.687
## 2         2 0.227 345.959
## 3         3 0.307 433.724
## 4         4 0.243 353.279
## 5         5 0.098 179.382
## 
##    variable       M      SD     min     max
## 1 moderator   3.083   1.289   1.000   6.000
## 2       wgt   0.200   0.087   0.098   0.307
## 3      Neff 300.206 111.548 179.382 433.724

5.3 Plot LSEM

Plotting the lsem.estimate for the first 20 indexes.

plot(lsem.MID, parindex=1:20)

5.4 Permutation Test LSEM

Running permutation test of LSEM model. In this case, using 10 permutation to save on time. In future iterations, permutations will be 1000.

lsem.permuted <- sirt::lsem.permutationTest(lsem.object = lsem.MID,
                                            B = 10, # permutations 
                                            residualize = FALSE) 
## Permutation test LSEM 
## 1  2  3  4  5  6  7  8  9  10
summary(lsem.permuted) # examine results
## -----------------------------------------------------------------
## Permutation Test for Local Structural Equation Model 
## 
## sirt 3.12-66 (2022-05-16 12:27:54) 
## lavaan 0.6-12 (2022-07-04 16:40:02 UTC) 
## 
## Function 'sirt::lsem.permutationTest' 
## 
## 
## Call:
## sirt::lsem.permutationTest(lsem.object = lsem.MID, B = 10, residualize = FALSE)
## 
## Date of Analysis: 2022-11-11 11:27:44 
## Time difference of 51.91566 secs
## Computation Time: 51.91566 
## 
## Number of permutations = 10 
## Percentage of non-converged datasets = 0 
## Number of observations=1000 
## Bandwidth factor=2 
## Bandwidth=0.648 
## Number of focal points for moderator=5 
## 
## lavaan Model
## 
## 
## # Factor loadings
## Approach =~ AWin_v_Neut_L_NAcc_run1  + AWin_v_Neut_R_NAcc_run1  + AWin_v_Neut_R_Insula_run1 +
##             AWin_v_Neut_L_NAcc_run2  + AWin_v_Neut_R_NAcc_run2 + AWin_v_Neut_R_Insula_run2 +
##             BWin_v_Neut_L_NAcc_run1  + BWin_v_Neut_R_NAcc_run1  + BWin_v_Neut_R_Insula_run1 +
##             BWin_v_Neut_L_NAcc_run2  + BWin_v_Neut_R_NAcc_run2  + BWin_v_Neut_R_Insula_run2 +
##             BWin_v_BLose_L_NAcc_run1 + BWin_v_BLose_R_NAcc_run1 +
##             BWin_v_BLose_L_NAcc_run2 + BWin_v_BLose_R_NAcc_run2 
##                 
## Avoid =~    ALose_v_Neut_L_Insula_run1 + ALose_v_Neut_R_Insula_run1 +
##             ALose_v_Neut_L_Insula_run2 + ALose_v_Neut_R_Insula_run2 +
##             BLose_v_Neut_L_Insula_run1 + BLose_v_Neut_R_Insula_run1 +
##             BLose_v_Neut_L_Insula_run2 + BLose_v_Neut_R_Insula_run2 +
##             BLose_v_BWin_L_Insula_run1 + BLose_v_BWin_R_Insula_run1 +
##             BLose_v_BWin_L_Insula_run2 + BLose_v_BWin_R_Insula_run2 
## 
## 
## Global Test Statistics
## 
##                                                       par      M    SD SD_p
## 1                       Approach=~AWin_v_Neut_L_NAcc_run1  0.082 0.006  0.6
## 2                       Approach=~AWin_v_Neut_R_NAcc_run1  0.086 0.004  0.9
## 3                     Approach=~AWin_v_Neut_R_Insula_run1  0.041 0.004  0.8
## 4                       Approach=~AWin_v_Neut_L_NAcc_run2  0.090 0.002  1.0
## 5                       Approach=~AWin_v_Neut_R_NAcc_run2  0.096 0.006  0.8
## 6                     Approach=~AWin_v_Neut_R_Insula_run2  0.049 0.007  0.3
## 7                       Approach=~BWin_v_Neut_L_NAcc_run1  0.095 0.009  0.2
## 8                       Approach=~BWin_v_Neut_R_NAcc_run1  0.070 0.007  0.2
## 9                     Approach=~BWin_v_Neut_R_Insula_run1  0.044 0.005  0.7
## 10                      Approach=~BWin_v_Neut_L_NAcc_run2  0.083 0.007  0.7
## 11                      Approach=~BWin_v_Neut_R_NAcc_run2  0.079 0.015  0.0
## 12                    Approach=~BWin_v_Neut_R_Insula_run2  0.050 0.011  0.1
## 13                     Approach=~BWin_v_BLose_L_NAcc_run1  0.092 0.006  0.6
## 14                     Approach=~BWin_v_BLose_R_NAcc_run1  0.089 0.005  0.8
## 15                     Approach=~BWin_v_BLose_L_NAcc_run2  0.079 0.008  0.5
## 16                     Approach=~BWin_v_BLose_R_NAcc_run2  0.095 0.004  1.0
## 17                      Avoid=~ALose_v_Neut_L_Insula_run1  0.087 0.003  1.0
## 18                      Avoid=~ALose_v_Neut_R_Insula_run1  0.094 0.009  0.4
## 19                      Avoid=~ALose_v_Neut_L_Insula_run2  0.078 0.008  0.4
## 20                      Avoid=~ALose_v_Neut_R_Insula_run2  0.090 0.012  0.2
## 21                      Avoid=~BLose_v_Neut_L_Insula_run1  0.086 0.013  0.0
## 22                      Avoid=~BLose_v_Neut_R_Insula_run1  0.092 0.006  0.7
## 23                      Avoid=~BLose_v_Neut_L_Insula_run2  0.082 0.006  0.7
## 24                      Avoid=~BLose_v_Neut_R_Insula_run2  0.091 0.005  0.8
## 25                      Avoid=~BLose_v_BWin_L_Insula_run1  0.085 0.016  0.1
## 26                      Avoid=~BLose_v_BWin_R_Insula_run1  0.040 0.010  0.1
## 27                      Avoid=~BLose_v_BWin_L_Insula_run2  0.077 0.014  0.0
## 28                      Avoid=~BLose_v_BWin_R_Insula_run2  0.041 0.004  0.7
## 29       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1  0.028 0.001  0.6
## 30       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1  0.031 0.002  0.2
## 31   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1  0.029 0.002  0.0
## 32       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2  0.027 0.001  0.8
## 33       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2  0.028 0.002  0.5
## 34   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2  0.028 0.002  0.3
## 35       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1  0.025 0.001  0.6
## 36       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1  0.029 0.001  0.8
## 37   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1  0.031 0.001  0.8
## 38       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2  0.030 0.001  0.7
## 39       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2  0.030 0.002  0.1
## 40   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2  0.031 0.001  0.8
## 41     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1  0.028 0.002  0.0
## 42     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1  0.030 0.003  0.1
## 43     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2  0.028 0.001  0.7
## 44     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2  0.028 0.002  0.0
## 45 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1  0.030 0.002  0.2
## 46 ALose_v_Neut_R_Insula_run1~~ALose_v_Neut_R_Insula_run1  0.027 0.002  0.1
## 47 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2  0.029 0.001  0.7
## 48 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2  0.029 0.003  0.0
## 49 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1  0.029 0.001  0.7
## 50 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1  0.025 0.001  0.9
## 51 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2  0.030 0.002  0.1
## 52 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2  0.029 0.002  0.5
## 53 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1  0.030 0.002  0.7
## 54 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1  0.031 0.002  0.0
## 55 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2  0.029 0.002  0.3
## 56 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2  0.029 0.001  1.0
## 57                                     Approach~~Approach  1.000 0.000  1.0
## 58                                           Avoid~~Avoid  1.000 0.000  1.0
## 59                                        Approach~~Avoid -0.577 0.037  0.6
## 60                              AWin_v_Neut_L_NAcc_run1~1 -0.003 0.016  0.0
## 61                              AWin_v_Neut_R_NAcc_run1~1 -0.004 0.009  0.2
## 62                            AWin_v_Neut_R_Insula_run1~1  0.007 0.004  0.6
## 63                              AWin_v_Neut_L_NAcc_run2~1 -0.002 0.009  0.1
## 64                              AWin_v_Neut_R_NAcc_run2~1  0.003 0.007  0.5
## 65                            AWin_v_Neut_R_Insula_run2~1  0.005 0.003  0.8
## 66                              BWin_v_Neut_L_NAcc_run1~1 -0.011 0.003  0.9
## 67                              BWin_v_Neut_R_NAcc_run1~1 -0.006 0.008  0.3
## 68                            BWin_v_Neut_R_Insula_run1~1  0.013 0.004  0.8
## 69                              BWin_v_Neut_L_NAcc_run2~1 -0.005 0.003  0.8
## 70                              BWin_v_Neut_R_NAcc_run2~1 -0.001 0.007  0.4
## 71                            BWin_v_Neut_R_Insula_run2~1 -0.001 0.006  0.5
## 72                             BWin_v_BLose_L_NAcc_run1~1 -0.003 0.009  0.3
## 73                             BWin_v_BLose_R_NAcc_run1~1 -0.005 0.011  0.1
## 74                             BWin_v_BLose_L_NAcc_run2~1 -0.008 0.010  0.0
## 75                             BWin_v_BLose_R_NAcc_run2~1 -0.008 0.008  0.1
## 76                           ALose_v_Neut_L_Insula_run1~1 -0.005 0.004  0.8
## 77                           ALose_v_Neut_R_Insula_run1~1  0.003 0.005  0.7
## 78                           ALose_v_Neut_L_Insula_run2~1 -0.001 0.005  0.8
## 79                           ALose_v_Neut_R_Insula_run2~1  0.002 0.005  0.8
## 80                           BLose_v_Neut_L_Insula_run1~1  0.002 0.009  0.0
## 81                           BLose_v_Neut_R_Insula_run1~1  0.014 0.008  0.5
## 82                           BLose_v_Neut_L_Insula_run2~1  0.013 0.003  0.9
## 83                           BLose_v_Neut_R_Insula_run2~1  0.005 0.006  0.4
## 84                           BLose_v_BWin_L_Insula_run1~1  0.008 0.006  0.3
## 85                           BLose_v_BWin_R_Insula_run1~1  0.002 0.005  0.7
## 86                           BLose_v_BWin_L_Insula_run2~1  0.005 0.004  0.7
## 87                           BLose_v_BWin_R_Insula_run2~1 -0.003 0.012  0.0
## 88                                             Approach~1  0.000 0.000  1.0
## 89                                                Avoid~1  0.000 0.000  1.0
## 90                                                  rmsea  0.075 0.005  0.7
## 91                                                    cfi  0.598 0.039  0.4
## 92                                                    tli  0.564 0.042  0.4
## 93                                                    gfi  0.860 0.014  0.6
## 94                                                   srmr  0.061 0.004  0.5
##      MAD MAD_p lin_slo lin_slo_p
## 1  0.006   0.5  -0.003       0.2
## 2  0.003   0.9   0.000       0.4
## 3  0.003   0.8  -0.001       0.8
## 4  0.002   1.0  -0.002       0.6
## 5  0.003   0.8  -0.004       0.6
## 6  0.006   0.2   0.005       0.2
## 7  0.005   0.4  -0.007       0.0
## 8  0.006   0.2   0.003       0.2
## 9  0.003   0.9  -0.004       0.8
## 10 0.005   0.8   0.001       1.0
## 11 0.012   0.0   0.013       0.0
## 12 0.009   0.1  -0.008       0.2
## 13 0.005   0.5  -0.003       0.4
## 14 0.004   0.8   0.002       0.8
## 15 0.005   0.5   0.003       0.6
## 16 0.003   1.0  -0.002       1.0
## 17 0.002   1.0   0.000       0.8
## 18 0.008   0.5   0.007       0.4
## 19 0.007   0.2  -0.006       0.2
## 20 0.009   0.4   0.004       0.8
## 21 0.012   0.0   0.006       0.2
## 22 0.005   0.6  -0.004       0.4
## 23 0.005   0.6   0.003       0.6
## 24 0.004   0.8   0.001       0.8
## 25 0.015   0.0   0.013       0.0
## 26 0.009   0.1  -0.006       0.0
## 27 0.012   0.1   0.011       0.0
## 28 0.004   0.7  -0.003       0.4
## 29 0.001   0.6   0.000       0.8
## 30 0.002   0.1   0.002       0.0
## 31 0.002   0.0   0.000       0.8
## 32 0.001   0.8   0.000       0.8
## 33 0.001   0.6   0.001       0.0
## 34 0.002   0.1  -0.002       0.0
## 35 0.001   0.9   0.001       0.4
## 36 0.001   0.6   0.000       0.8
## 37 0.001   0.6  -0.001       0.2
## 38 0.001   0.7  -0.001       0.8
## 39 0.001   0.3  -0.001       0.2
## 40 0.001   0.6   0.000       1.0
## 41 0.001   0.3  -0.001       0.2
## 42 0.002   0.1  -0.002       0.0
## 43 0.001   0.6  -0.001       0.4
## 44 0.002   0.0   0.002       0.0
## 45 0.002   0.1  -0.001       0.8
## 46 0.002   0.1  -0.002       0.2
## 47 0.001   0.7   0.000       1.0
## 48 0.003   0.0  -0.002       0.0
## 49 0.001   0.7  -0.001       0.4
## 50 0.001   0.8   0.000       1.0
## 51 0.002   0.1   0.000       0.8
## 52 0.001   0.7   0.002       0.2
## 53 0.002   0.6  -0.001       0.4
## 54 0.002   0.0  -0.002       0.0
## 55 0.001   0.3  -0.001       0.0
## 56 0.001   0.9   0.000       1.0
## 57 0.000   1.0   0.000       1.0
## 58 0.000   1.0   0.000       1.0
## 59 0.033   0.6  -0.020       0.2
## 60 0.014   0.0  -0.013       0.0
## 61 0.008   0.2  -0.002       0.2
## 62 0.003   0.6   0.001       1.0
## 63 0.007   0.0  -0.007       0.0
## 64 0.005   0.4  -0.004       0.2
## 65 0.003   0.5  -0.002       0.0
## 66 0.003   0.9   0.001       0.8
## 67 0.006   0.3  -0.004       0.6
## 68 0.003   0.7   0.002       0.2
## 69 0.003   0.8   0.001       0.8
## 70 0.005   0.6  -0.004       0.0
## 71 0.004   0.6  -0.004       0.2
## 72 0.007   0.3  -0.003       0.6
## 73 0.010   0.0  -0.008       0.0
## 74 0.010   0.0  -0.005       0.2
## 75 0.008   0.0  -0.004       0.0
## 76 0.004   0.8   0.001       0.6
## 77 0.004   0.6  -0.004       0.0
## 78 0.004   0.7   0.001       0.8
## 79 0.003   0.9  -0.002       0.8
## 80 0.007   0.2  -0.003       0.4
## 81 0.007   0.3   0.007       0.0
## 82 0.003   0.8   0.001       0.6
## 83 0.006   0.1   0.002       0.2
## 84 0.005   0.3  -0.003       0.2
## 85 0.003   0.8  -0.002       0.6
## 86 0.003   0.7  -0.001       1.0
## 87 0.010   0.0   0.008       0.0
## 88 0.000   1.0   0.000       1.0
## 89 0.000   1.0   0.000       1.0
## 90 0.005   0.2   0.001       0.0
## 91 0.030   0.5   0.001       0.8
## 92 0.033   0.5   0.001       0.8
## 93 0.013   0.3  -0.004       0.0
## 94 0.003   0.4   0.000       0.6
## 
## Pointwise Test Statistics
## 
##                                                        par parindex moderator
## 1                        Approach=~AWin_v_Neut_L_NAcc_run1        1         1
## 2                        Approach=~AWin_v_Neut_L_NAcc_run1        1         2
## 3                        Approach=~AWin_v_Neut_L_NAcc_run1        1         3
## 4                        Approach=~AWin_v_Neut_L_NAcc_run1        1         4
## 5                        Approach=~AWin_v_Neut_L_NAcc_run1        1         5
## 6                        Approach=~AWin_v_Neut_R_NAcc_run1        2         1
## 7                        Approach=~AWin_v_Neut_R_NAcc_run1        2         2
## 8                        Approach=~AWin_v_Neut_R_NAcc_run1        2         3
## 9                        Approach=~AWin_v_Neut_R_NAcc_run1        2         4
## 10                       Approach=~AWin_v_Neut_R_NAcc_run1        2         5
## 11                     Approach=~AWin_v_Neut_R_Insula_run1        3         1
## 12                     Approach=~AWin_v_Neut_R_Insula_run1        3         2
## 13                     Approach=~AWin_v_Neut_R_Insula_run1        3         3
## 14                     Approach=~AWin_v_Neut_R_Insula_run1        3         4
## 15                     Approach=~AWin_v_Neut_R_Insula_run1        3         5
## 16                       Approach=~AWin_v_Neut_L_NAcc_run2        4         1
## 17                       Approach=~AWin_v_Neut_L_NAcc_run2        4         2
## 18                       Approach=~AWin_v_Neut_L_NAcc_run2        4         3
## 19                       Approach=~AWin_v_Neut_L_NAcc_run2        4         4
## 20                       Approach=~AWin_v_Neut_L_NAcc_run2        4         5
## 21                       Approach=~AWin_v_Neut_R_NAcc_run2        5         1
## 22                       Approach=~AWin_v_Neut_R_NAcc_run2        5         2
## 23                       Approach=~AWin_v_Neut_R_NAcc_run2        5         3
## 24                       Approach=~AWin_v_Neut_R_NAcc_run2        5         4
## 25                       Approach=~AWin_v_Neut_R_NAcc_run2        5         5
## 26                     Approach=~AWin_v_Neut_R_Insula_run2        6         1
## 27                     Approach=~AWin_v_Neut_R_Insula_run2        6         2
## 28                     Approach=~AWin_v_Neut_R_Insula_run2        6         3
## 29                     Approach=~AWin_v_Neut_R_Insula_run2        6         4
## 30                     Approach=~AWin_v_Neut_R_Insula_run2        6         5
## 31                       Approach=~BWin_v_Neut_L_NAcc_run1        7         1
## 32                       Approach=~BWin_v_Neut_L_NAcc_run1        7         2
## 33                       Approach=~BWin_v_Neut_L_NAcc_run1        7         3
## 34                       Approach=~BWin_v_Neut_L_NAcc_run1        7         4
## 35                       Approach=~BWin_v_Neut_L_NAcc_run1        7         5
## 36                       Approach=~BWin_v_Neut_R_NAcc_run1        8         1
## 37                       Approach=~BWin_v_Neut_R_NAcc_run1        8         2
## 38                       Approach=~BWin_v_Neut_R_NAcc_run1        8         3
## 39                       Approach=~BWin_v_Neut_R_NAcc_run1        8         4
## 40                       Approach=~BWin_v_Neut_R_NAcc_run1        8         5
## 41                     Approach=~BWin_v_Neut_R_Insula_run1        9         1
## 42                     Approach=~BWin_v_Neut_R_Insula_run1        9         2
## 43                     Approach=~BWin_v_Neut_R_Insula_run1        9         3
## 44                     Approach=~BWin_v_Neut_R_Insula_run1        9         4
## 45                     Approach=~BWin_v_Neut_R_Insula_run1        9         5
## 46                       Approach=~BWin_v_Neut_L_NAcc_run2       10         1
## 47                       Approach=~BWin_v_Neut_L_NAcc_run2       10         2
## 48                       Approach=~BWin_v_Neut_L_NAcc_run2       10         3
## 49                       Approach=~BWin_v_Neut_L_NAcc_run2       10         4
## 50                       Approach=~BWin_v_Neut_L_NAcc_run2       10         5
## 51                       Approach=~BWin_v_Neut_R_NAcc_run2       11         1
## 52                       Approach=~BWin_v_Neut_R_NAcc_run2       11         2
## 53                       Approach=~BWin_v_Neut_R_NAcc_run2       11         3
## 54                       Approach=~BWin_v_Neut_R_NAcc_run2       11         4
## 55                       Approach=~BWin_v_Neut_R_NAcc_run2       11         5
## 56                     Approach=~BWin_v_Neut_R_Insula_run2       12         1
## 57                     Approach=~BWin_v_Neut_R_Insula_run2       12         2
## 58                     Approach=~BWin_v_Neut_R_Insula_run2       12         3
## 59                     Approach=~BWin_v_Neut_R_Insula_run2       12         4
## 60                     Approach=~BWin_v_Neut_R_Insula_run2       12         5
## 61                      Approach=~BWin_v_BLose_L_NAcc_run1       13         1
## 62                      Approach=~BWin_v_BLose_L_NAcc_run1       13         2
## 63                      Approach=~BWin_v_BLose_L_NAcc_run1       13         3
## 64                      Approach=~BWin_v_BLose_L_NAcc_run1       13         4
## 65                      Approach=~BWin_v_BLose_L_NAcc_run1       13         5
## 66                      Approach=~BWin_v_BLose_R_NAcc_run1       14         1
## 67                      Approach=~BWin_v_BLose_R_NAcc_run1       14         2
## 68                      Approach=~BWin_v_BLose_R_NAcc_run1       14         3
## 69                      Approach=~BWin_v_BLose_R_NAcc_run1       14         4
## 70                      Approach=~BWin_v_BLose_R_NAcc_run1       14         5
## 71                      Approach=~BWin_v_BLose_L_NAcc_run2       15         1
## 72                      Approach=~BWin_v_BLose_L_NAcc_run2       15         2
## 73                      Approach=~BWin_v_BLose_L_NAcc_run2       15         3
## 74                      Approach=~BWin_v_BLose_L_NAcc_run2       15         4
## 75                      Approach=~BWin_v_BLose_L_NAcc_run2       15         5
## 76                      Approach=~BWin_v_BLose_R_NAcc_run2       16         1
## 77                      Approach=~BWin_v_BLose_R_NAcc_run2       16         2
## 78                      Approach=~BWin_v_BLose_R_NAcc_run2       16         3
## 79                      Approach=~BWin_v_BLose_R_NAcc_run2       16         4
## 80                      Approach=~BWin_v_BLose_R_NAcc_run2       16         5
## 81                       Avoid=~ALose_v_Neut_L_Insula_run1       17         1
## 82                       Avoid=~ALose_v_Neut_L_Insula_run1       17         2
## 83                       Avoid=~ALose_v_Neut_L_Insula_run1       17         3
## 84                       Avoid=~ALose_v_Neut_L_Insula_run1       17         4
## 85                       Avoid=~ALose_v_Neut_L_Insula_run1       17         5
## 86                       Avoid=~ALose_v_Neut_R_Insula_run1       18         1
## 87                       Avoid=~ALose_v_Neut_R_Insula_run1       18         2
## 88                       Avoid=~ALose_v_Neut_R_Insula_run1       18         3
## 89                       Avoid=~ALose_v_Neut_R_Insula_run1       18         4
## 90                       Avoid=~ALose_v_Neut_R_Insula_run1       18         5
## 91                       Avoid=~ALose_v_Neut_L_Insula_run2       19         1
## 92                       Avoid=~ALose_v_Neut_L_Insula_run2       19         2
## 93                       Avoid=~ALose_v_Neut_L_Insula_run2       19         3
## 94                       Avoid=~ALose_v_Neut_L_Insula_run2       19         4
## 95                       Avoid=~ALose_v_Neut_L_Insula_run2       19         5
## 96                       Avoid=~ALose_v_Neut_R_Insula_run2       20         1
## 97                       Avoid=~ALose_v_Neut_R_Insula_run2       20         2
## 98                       Avoid=~ALose_v_Neut_R_Insula_run2       20         3
## 99                       Avoid=~ALose_v_Neut_R_Insula_run2       20         4
## 100                      Avoid=~ALose_v_Neut_R_Insula_run2       20         5
## 101                      Avoid=~BLose_v_Neut_L_Insula_run1       21         1
## 102                      Avoid=~BLose_v_Neut_L_Insula_run1       21         2
## 103                      Avoid=~BLose_v_Neut_L_Insula_run1       21         3
## 104                      Avoid=~BLose_v_Neut_L_Insula_run1       21         4
## 105                      Avoid=~BLose_v_Neut_L_Insula_run1       21         5
## 106                      Avoid=~BLose_v_Neut_R_Insula_run1       22         1
## 107                      Avoid=~BLose_v_Neut_R_Insula_run1       22         2
## 108                      Avoid=~BLose_v_Neut_R_Insula_run1       22         3
## 109                      Avoid=~BLose_v_Neut_R_Insula_run1       22         4
## 110                      Avoid=~BLose_v_Neut_R_Insula_run1       22         5
## 111                      Avoid=~BLose_v_Neut_L_Insula_run2       23         1
## 112                      Avoid=~BLose_v_Neut_L_Insula_run2       23         2
## 113                      Avoid=~BLose_v_Neut_L_Insula_run2       23         3
## 114                      Avoid=~BLose_v_Neut_L_Insula_run2       23         4
## 115                      Avoid=~BLose_v_Neut_L_Insula_run2       23         5
## 116                      Avoid=~BLose_v_Neut_R_Insula_run2       24         1
## 117                      Avoid=~BLose_v_Neut_R_Insula_run2       24         2
## 118                      Avoid=~BLose_v_Neut_R_Insula_run2       24         3
## 119                      Avoid=~BLose_v_Neut_R_Insula_run2       24         4
## 120                      Avoid=~BLose_v_Neut_R_Insula_run2       24         5
## 121                      Avoid=~BLose_v_BWin_L_Insula_run1       25         1
## 122                      Avoid=~BLose_v_BWin_L_Insula_run1       25         2
## 123                      Avoid=~BLose_v_BWin_L_Insula_run1       25         3
## 124                      Avoid=~BLose_v_BWin_L_Insula_run1       25         4
## 125                      Avoid=~BLose_v_BWin_L_Insula_run1       25         5
## 126                      Avoid=~BLose_v_BWin_R_Insula_run1       26         1
## 127                      Avoid=~BLose_v_BWin_R_Insula_run1       26         2
## 128                      Avoid=~BLose_v_BWin_R_Insula_run1       26         3
## 129                      Avoid=~BLose_v_BWin_R_Insula_run1       26         4
## 130                      Avoid=~BLose_v_BWin_R_Insula_run1       26         5
## 131                      Avoid=~BLose_v_BWin_L_Insula_run2       27         1
## 132                      Avoid=~BLose_v_BWin_L_Insula_run2       27         2
## 133                      Avoid=~BLose_v_BWin_L_Insula_run2       27         3
## 134                      Avoid=~BLose_v_BWin_L_Insula_run2       27         4
## 135                      Avoid=~BLose_v_BWin_L_Insula_run2       27         5
## 136                      Avoid=~BLose_v_BWin_R_Insula_run2       28         1
## 137                      Avoid=~BLose_v_BWin_R_Insula_run2       28         2
## 138                      Avoid=~BLose_v_BWin_R_Insula_run2       28         3
## 139                      Avoid=~BLose_v_BWin_R_Insula_run2       28         4
## 140                      Avoid=~BLose_v_BWin_R_Insula_run2       28         5
## 141       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       29         1
## 142       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       29         2
## 143       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       29         3
## 144       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       29         4
## 145       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       29         5
## 146       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       30         1
## 147       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       30         2
## 148       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       30         3
## 149       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       30         4
## 150       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       30         5
## 151   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       31         1
## 152   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       31         2
## 153   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       31         3
## 154   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       31         4
## 155   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       31         5
## 156       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       32         1
## 157       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       32         2
## 158       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       32         3
## 159       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       32         4
## 160       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       32         5
## 161       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       33         1
## 162       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       33         2
## 163       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       33         3
## 164       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       33         4
## 165       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       33         5
## 166   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       34         1
## 167   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       34         2
## 168   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       34         3
## 169   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       34         4
## 170   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       34         5
## 171       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       35         1
## 172       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       35         2
## 173       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       35         3
## 174       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       35         4
## 175       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       35         5
## 176       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       36         1
## 177       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       36         2
## 178       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       36         3
## 179       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       36         4
## 180       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       36         5
## 181   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       37         1
## 182   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       37         2
## 183   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       37         3
## 184   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       37         4
## 185   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       37         5
## 186       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       38         1
## 187       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       38         2
## 188       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       38         3
## 189       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       38         4
## 190       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       38         5
## 191       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       39         1
## 192       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       39         2
## 193       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       39         3
## 194       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       39         4
## 195       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       39         5
## 196   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       40         1
## 197   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       40         2
## 198   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       40         3
## 199   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       40         4
## 200   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       40         5
## 201     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       41         1
## 202     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       41         2
## 203     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       41         3
## 204     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       41         4
## 205     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       41         5
## 206     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       42         1
## 207     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       42         2
## 208     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       42         3
## 209     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       42         4
## 210     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       42         5
## 211     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       43         1
## 212     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       43         2
## 213     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       43         3
## 214     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       43         4
## 215     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       43         5
## 216     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       44         1
## 217     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       44         2
## 218     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       44         3
## 219     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       44         4
## 220     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       44         5
## 221 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       45         1
## 222 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       45         2
## 223 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       45         3
## 224 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       45         4
## 225 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       45         5
## 226 ALose_v_Neut_R_Insula_run1~~ALose_v_Neut_R_Insula_run1       46         1
## 227 ALose_v_Neut_R_Insula_run1~~ALose_v_Neut_R_Insula_run1       46         2
## 228 ALose_v_Neut_R_Insula_run1~~ALose_v_Neut_R_Insula_run1       46         3
## 229 ALose_v_Neut_R_Insula_run1~~ALose_v_Neut_R_Insula_run1       46         4
## 230 ALose_v_Neut_R_Insula_run1~~ALose_v_Neut_R_Insula_run1       46         5
## 231 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       47         1
## 232 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       47         2
## 233 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       47         3
## 234 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       47         4
## 235 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       47         5
## 236 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       48         1
## 237 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       48         2
## 238 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       48         3
## 239 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       48         4
## 240 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       48         5
## 241 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       49         1
## 242 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       49         2
## 243 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       49         3
## 244 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       49         4
## 245 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       49         5
## 246 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       50         1
## 247 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       50         2
## 248 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       50         3
## 249 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       50         4
## 250 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       50         5
## 251 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         1
## 252 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         2
## 253 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         3
## 254 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         4
## 255 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         5
## 256 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         1
## 257 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         2
## 258 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         3
## 259 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         4
## 260 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         5
## 261 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       53         1
## 262 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       53         2
## 263 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       53         3
## 264 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       53         4
## 265 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       53         5
## 266 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       54         1
## 267 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       54         2
## 268 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       54         3
## 269 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       54         4
## 270 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       54         5
## 271 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       55         1
## 272 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       55         2
## 273 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       55         3
## 274 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       55         4
## 275 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       55         5
## 276 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       56         1
## 277 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       56         2
## 278 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       56         3
## 279 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       56         4
## 280 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       56         5
## 281                                     Approach~~Approach       57         1
## 282                                     Approach~~Approach       57         2
## 283                                     Approach~~Approach       57         3
## 284                                     Approach~~Approach       57         4
## 285                                     Approach~~Approach       57         5
## 286                                           Avoid~~Avoid       58         1
## 287                                           Avoid~~Avoid       58         2
## 288                                           Avoid~~Avoid       58         3
## 289                                           Avoid~~Avoid       58         4
## 290                                           Avoid~~Avoid       58         5
## 291                                        Approach~~Avoid       59         1
## 292                                        Approach~~Avoid       59         2
## 293                                        Approach~~Avoid       59         3
## 294                                        Approach~~Avoid       59         4
## 295                                        Approach~~Avoid       59         5
## 296                              AWin_v_Neut_L_NAcc_run1~1       60         1
## 297                              AWin_v_Neut_L_NAcc_run1~1       60         2
## 298                              AWin_v_Neut_L_NAcc_run1~1       60         3
## 299                              AWin_v_Neut_L_NAcc_run1~1       60         4
## 300                              AWin_v_Neut_L_NAcc_run1~1       60         5
## 301                              AWin_v_Neut_R_NAcc_run1~1       61         1
## 302                              AWin_v_Neut_R_NAcc_run1~1       61         2
## 303                              AWin_v_Neut_R_NAcc_run1~1       61         3
## 304                              AWin_v_Neut_R_NAcc_run1~1       61         4
## 305                              AWin_v_Neut_R_NAcc_run1~1       61         5
## 306                            AWin_v_Neut_R_Insula_run1~1       62         1
## 307                            AWin_v_Neut_R_Insula_run1~1       62         2
## 308                            AWin_v_Neut_R_Insula_run1~1       62         3
## 309                            AWin_v_Neut_R_Insula_run1~1       62         4
## 310                            AWin_v_Neut_R_Insula_run1~1       62         5
## 311                              AWin_v_Neut_L_NAcc_run2~1       63         1
## 312                              AWin_v_Neut_L_NAcc_run2~1       63         2
## 313                              AWin_v_Neut_L_NAcc_run2~1       63         3
## 314                              AWin_v_Neut_L_NAcc_run2~1       63         4
## 315                              AWin_v_Neut_L_NAcc_run2~1       63         5
## 316                              AWin_v_Neut_R_NAcc_run2~1       64         1
## 317                              AWin_v_Neut_R_NAcc_run2~1       64         2
## 318                              AWin_v_Neut_R_NAcc_run2~1       64         3
## 319                              AWin_v_Neut_R_NAcc_run2~1       64         4
## 320                              AWin_v_Neut_R_NAcc_run2~1       64         5
## 321                            AWin_v_Neut_R_Insula_run2~1       65         1
## 322                            AWin_v_Neut_R_Insula_run2~1       65         2
## 323                            AWin_v_Neut_R_Insula_run2~1       65         3
## 324                            AWin_v_Neut_R_Insula_run2~1       65         4
## 325                            AWin_v_Neut_R_Insula_run2~1       65         5
## 326                              BWin_v_Neut_L_NAcc_run1~1       66         1
## 327                              BWin_v_Neut_L_NAcc_run1~1       66         2
## 328                              BWin_v_Neut_L_NAcc_run1~1       66         3
## 329                              BWin_v_Neut_L_NAcc_run1~1       66         4
## 330                              BWin_v_Neut_L_NAcc_run1~1       66         5
## 331                              BWin_v_Neut_R_NAcc_run1~1       67         1
## 332                              BWin_v_Neut_R_NAcc_run1~1       67         2
## 333                              BWin_v_Neut_R_NAcc_run1~1       67         3
## 334                              BWin_v_Neut_R_NAcc_run1~1       67         4
## 335                              BWin_v_Neut_R_NAcc_run1~1       67         5
## 336                            BWin_v_Neut_R_Insula_run1~1       68         1
## 337                            BWin_v_Neut_R_Insula_run1~1       68         2
## 338                            BWin_v_Neut_R_Insula_run1~1       68         3
## 339                            BWin_v_Neut_R_Insula_run1~1       68         4
## 340                            BWin_v_Neut_R_Insula_run1~1       68         5
## 341                              BWin_v_Neut_L_NAcc_run2~1       69         1
## 342                              BWin_v_Neut_L_NAcc_run2~1       69         2
## 343                              BWin_v_Neut_L_NAcc_run2~1       69         3
## 344                              BWin_v_Neut_L_NAcc_run2~1       69         4
## 345                              BWin_v_Neut_L_NAcc_run2~1       69         5
## 346                              BWin_v_Neut_R_NAcc_run2~1       70         1
## 347                              BWin_v_Neut_R_NAcc_run2~1       70         2
## 348                              BWin_v_Neut_R_NAcc_run2~1       70         3
## 349                              BWin_v_Neut_R_NAcc_run2~1       70         4
## 350                              BWin_v_Neut_R_NAcc_run2~1       70         5
## 351                            BWin_v_Neut_R_Insula_run2~1       71         1
## 352                            BWin_v_Neut_R_Insula_run2~1       71         2
## 353                            BWin_v_Neut_R_Insula_run2~1       71         3
## 354                            BWin_v_Neut_R_Insula_run2~1       71         4
## 355                            BWin_v_Neut_R_Insula_run2~1       71         5
## 356                             BWin_v_BLose_L_NAcc_run1~1       72         1
## 357                             BWin_v_BLose_L_NAcc_run1~1       72         2
## 358                             BWin_v_BLose_L_NAcc_run1~1       72         3
## 359                             BWin_v_BLose_L_NAcc_run1~1       72         4
## 360                             BWin_v_BLose_L_NAcc_run1~1       72         5
## 361                             BWin_v_BLose_R_NAcc_run1~1       73         1
## 362                             BWin_v_BLose_R_NAcc_run1~1       73         2
## 363                             BWin_v_BLose_R_NAcc_run1~1       73         3
## 364                             BWin_v_BLose_R_NAcc_run1~1       73         4
## 365                             BWin_v_BLose_R_NAcc_run1~1       73         5
## 366                             BWin_v_BLose_L_NAcc_run2~1       74         1
## 367                             BWin_v_BLose_L_NAcc_run2~1       74         2
## 368                             BWin_v_BLose_L_NAcc_run2~1       74         3
## 369                             BWin_v_BLose_L_NAcc_run2~1       74         4
## 370                             BWin_v_BLose_L_NAcc_run2~1       74         5
## 371                             BWin_v_BLose_R_NAcc_run2~1       75         1
## 372                             BWin_v_BLose_R_NAcc_run2~1       75         2
## 373                             BWin_v_BLose_R_NAcc_run2~1       75         3
## 374                             BWin_v_BLose_R_NAcc_run2~1       75         4
## 375                             BWin_v_BLose_R_NAcc_run2~1       75         5
## 376                           ALose_v_Neut_L_Insula_run1~1       76         1
## 377                           ALose_v_Neut_L_Insula_run1~1       76         2
## 378                           ALose_v_Neut_L_Insula_run1~1       76         3
## 379                           ALose_v_Neut_L_Insula_run1~1       76         4
## 380                           ALose_v_Neut_L_Insula_run1~1       76         5
## 381                           ALose_v_Neut_R_Insula_run1~1       77         1
## 382                           ALose_v_Neut_R_Insula_run1~1       77         2
## 383                           ALose_v_Neut_R_Insula_run1~1       77         3
## 384                           ALose_v_Neut_R_Insula_run1~1       77         4
## 385                           ALose_v_Neut_R_Insula_run1~1       77         5
## 386                           ALose_v_Neut_L_Insula_run2~1       78         1
## 387                           ALose_v_Neut_L_Insula_run2~1       78         2
## 388                           ALose_v_Neut_L_Insula_run2~1       78         3
## 389                           ALose_v_Neut_L_Insula_run2~1       78         4
## 390                           ALose_v_Neut_L_Insula_run2~1       78         5
## 391                           ALose_v_Neut_R_Insula_run2~1       79         1
## 392                           ALose_v_Neut_R_Insula_run2~1       79         2
## 393                           ALose_v_Neut_R_Insula_run2~1       79         3
## 394                           ALose_v_Neut_R_Insula_run2~1       79         4
## 395                           ALose_v_Neut_R_Insula_run2~1       79         5
## 396                           BLose_v_Neut_L_Insula_run1~1       80         1
## 397                           BLose_v_Neut_L_Insula_run1~1       80         2
## 398                           BLose_v_Neut_L_Insula_run1~1       80         3
## 399                           BLose_v_Neut_L_Insula_run1~1       80         4
## 400                           BLose_v_Neut_L_Insula_run1~1       80         5
## 401                           BLose_v_Neut_R_Insula_run1~1       81         1
## 402                           BLose_v_Neut_R_Insula_run1~1       81         2
## 403                           BLose_v_Neut_R_Insula_run1~1       81         3
## 404                           BLose_v_Neut_R_Insula_run1~1       81         4
## 405                           BLose_v_Neut_R_Insula_run1~1       81         5
## 406                           BLose_v_Neut_L_Insula_run2~1       82         1
## 407                           BLose_v_Neut_L_Insula_run2~1       82         2
## 408                           BLose_v_Neut_L_Insula_run2~1       82         3
## 409                           BLose_v_Neut_L_Insula_run2~1       82         4
## 410                           BLose_v_Neut_L_Insula_run2~1       82         5
## 411                           BLose_v_Neut_R_Insula_run2~1       83         1
## 412                           BLose_v_Neut_R_Insula_run2~1       83         2
## 413                           BLose_v_Neut_R_Insula_run2~1       83         3
## 414                           BLose_v_Neut_R_Insula_run2~1       83         4
## 415                           BLose_v_Neut_R_Insula_run2~1       83         5
## 416                           BLose_v_BWin_L_Insula_run1~1       84         1
## 417                           BLose_v_BWin_L_Insula_run1~1       84         2
## 418                           BLose_v_BWin_L_Insula_run1~1       84         3
## 419                           BLose_v_BWin_L_Insula_run1~1       84         4
## 420                           BLose_v_BWin_L_Insula_run1~1       84         5
## 421                           BLose_v_BWin_R_Insula_run1~1       85         1
## 422                           BLose_v_BWin_R_Insula_run1~1       85         2
## 423                           BLose_v_BWin_R_Insula_run1~1       85         3
## 424                           BLose_v_BWin_R_Insula_run1~1       85         4
## 425                           BLose_v_BWin_R_Insula_run1~1       85         5
## 426                           BLose_v_BWin_L_Insula_run2~1       86         1
## 427                           BLose_v_BWin_L_Insula_run2~1       86         2
## 428                           BLose_v_BWin_L_Insula_run2~1       86         3
## 429                           BLose_v_BWin_L_Insula_run2~1       86         4
## 430                           BLose_v_BWin_L_Insula_run2~1       86         5
## 431                           BLose_v_BWin_R_Insula_run2~1       87         1
## 432                           BLose_v_BWin_R_Insula_run2~1       87         2
## 433                           BLose_v_BWin_R_Insula_run2~1       87         3
## 434                           BLose_v_BWin_R_Insula_run2~1       87         4
## 435                           BLose_v_BWin_R_Insula_run2~1       87         5
## 436                                             Approach~1       88         1
## 437                                             Approach~1       88         2
## 438                                             Approach~1       88         3
## 439                                             Approach~1       88         4
## 440                                             Approach~1       88         5
## 441                                                Avoid~1       89         1
## 442                                                Avoid~1       89         2
## 443                                                Avoid~1       89         3
## 444                                                Avoid~1       89         4
## 445                                                Avoid~1       89         5
## 446                                                  rmsea       90         1
## 447                                                  rmsea       90         2
## 448                                                  rmsea       90         3
## 449                                                  rmsea       90         4
## 450                                                  rmsea       90         5
## 451                                                    cfi       91         1
## 452                                                    cfi       91         2
## 453                                                    cfi       91         3
## 454                                                    cfi       91         4
## 455                                                    cfi       91         5
## 456                                                    tli       92         1
## 457                                                    tli       92         2
## 458                                                    tli       92         3
## 459                                                    tli       92         4
## 460                                                    tli       92         5
## 461                                                    gfi       93         1
## 462                                                    gfi       93         2
## 463                                                    gfi       93         3
## 464                                                    gfi       93         4
## 465                                                    gfi       93         5
## 466                                                   srmr       94         1
## 467                                                   srmr       94         2
## 468                                                   srmr       94         3
## 469                                                   srmr       94         4
## 470                                                   srmr       94         5
##        est   p
## 1   -0.002 0.8
## 2    0.009 0.4
## 3    0.003 0.6
## 4   -0.008 0.4
## 5   -0.007 0.0
## 6    0.006 0.2
## 7   -0.004 0.6
## 8    0.000 0.8
## 9    0.003 1.0
## 10  -0.004 0.8
## 11   0.007 0.4
## 12   0.001 0.8
## 13  -0.005 0.6
## 14   0.001 0.8
## 15   0.002 0.8
## 16   0.001 0.6
## 17   0.003 0.6
## 18   0.001 1.0
## 19  -0.002 0.4
## 20  -0.006 0.4
## 21   0.014 0.2
## 22  -0.001 0.8
## 23  -0.001 0.2
## 24  -0.001 0.8
## 25  -0.010 0.6
## 26  -0.011 0.0
## 27  -0.002 1.0
## 28  -0.004 0.4
## 29   0.008 0.0
## 30   0.012 0.2
## 31   0.011 0.4
## 32   0.006 0.4
## 33   0.000 1.0
## 34  -0.001 0.6
## 35  -0.024 0.0
## 36  -0.006 0.8
## 37  -0.008 0.0
## 38   0.002 0.6
## 39   0.010 0.0
## 40  -0.005 1.0
## 41   0.010 0.6
## 42  -0.001 1.0
## 43   0.001 0.6
## 44  -0.002 1.0
## 45  -0.011 0.8
## 46  -0.008 0.8
## 47  -0.002 0.8
## 48   0.003 0.6
## 49   0.008 0.4
## 50  -0.014 0.2
## 51  -0.023 0.0
## 52  -0.014 0.0
## 53   0.000 1.0
## 54   0.016 0.0
## 55   0.021 0.2
## 56   0.022 0.0
## 57   0.000 0.8
## 58   0.005 0.0
## 59  -0.012 0.0
## 60  -0.013 0.4
## 61  -0.001 0.8
## 62   0.003 0.6
## 63   0.005 0.6
## 64  -0.003 0.8
## 65  -0.015 0.0
## 66   0.004 0.8
## 67  -0.006 0.2
## 68  -0.002 1.0
## 69   0.002 0.6
## 70   0.011 0.4
## 71  -0.018 0.2
## 72   0.001 0.4
## 73   0.006 0.6
## 74   0.001 0.8
## 75  -0.002 0.8
## 76   0.004 0.8
## 77   0.002 0.8
## 78  -0.002 1.0
## 79   0.002 0.8
## 80  -0.009 0.8
## 81  -0.005 0.8
## 82   0.005 1.0
## 83   0.000 1.0
## 84  -0.002 0.8
## 85   0.001 0.8
## 86  -0.014 0.4
## 87  -0.010 0.4
## 88   0.002 0.8
## 89   0.010 0.2
## 90   0.009 0.4
## 91   0.009 0.8
## 92   0.010 0.2
## 93  -0.001 0.8
## 94  -0.009 0.2
## 95  -0.009 0.4
## 96  -0.023 0.2
## 97  -0.004 1.0
## 98   0.014 0.0
## 99   0.001 0.8
## 100 -0.007 0.6
## 101 -0.028 0.0
## 102 -0.006 0.6
## 103  0.011 0.0
## 104  0.010 0.4
## 105 -0.010 0.4
## 106  0.006 0.6
## 107  0.003 0.6
## 108  0.003 0.6
## 109 -0.009 0.2
## 110 -0.002 1.0
## 111 -0.011 0.6
## 112 -0.004 0.6
## 113  0.006 0.2
## 114  0.003 0.8
## 115 -0.003 0.6
## 116 -0.010 0.4
## 117  0.002 0.8
## 118  0.003 0.6
## 119  0.002 0.8
## 120 -0.006 1.0
## 121 -0.023 0.0
## 122 -0.021 0.0
## 123  0.006 0.4
## 124  0.019 0.0
## 125  0.011 0.0
## 126  0.016 0.0
## 127  0.009 0.4
## 128 -0.006 0.0
## 129 -0.012 0.0
## 130  0.007 0.4
## 131 -0.013 0.2
## 132 -0.020 0.0
## 133  0.001 1.0
## 134  0.015 0.0
## 135  0.020 0.4
## 136  0.009 0.2
## 137  0.003 0.4
## 138 -0.003 0.6
## 139 -0.004 0.4
## 140  0.000 0.8
## 141 -0.002 0.6
## 142 -0.001 1.0
## 143  0.001 0.0
## 144  0.001 0.8
## 145 -0.001 0.6
## 146 -0.003 0.2
## 147 -0.002 0.0
## 148  0.001 0.8
## 149  0.002 0.0
## 150  0.002 0.4
## 151  0.003 0.0
## 152  0.000 0.8
## 153 -0.002 0.0
## 154  0.001 0.4
## 155  0.002 0.2
## 156 -0.002 0.6
## 157  0.001 1.0
## 158  0.000 0.6
## 159  0.000 0.8
## 160 -0.001 0.8
## 161  0.000 0.4
## 162 -0.001 0.4
## 163 -0.001 0.8
## 164  0.001 0.4
## 165  0.004 0.0
## 166  0.004 0.2
## 167  0.002 0.2
## 168 -0.001 0.4
## 169 -0.002 0.2
## 170 -0.003 0.0
## 171 -0.001 0.6
## 172  0.000 0.8
## 173  0.000 0.6
## 174  0.000 0.8
## 175  0.003 0.0
## 176 -0.001 0.6
## 177  0.001 0.8
## 178  0.000 0.6
## 179  0.001 0.4
## 180 -0.002 0.6
## 181  0.001 0.6
## 182  0.001 0.0
## 183 -0.001 0.6
## 184  0.000 0.8
## 185 -0.001 0.4
## 186  0.000 0.8
## 187  0.001 0.8
## 188  0.001 0.6
## 189 -0.002 0.4
## 190 -0.002 0.8
## 191  0.000 0.4
## 192  0.001 0.4
## 193  0.002 0.0
## 194 -0.001 0.2
## 195 -0.005 0.2
## 196 -0.001 0.4
## 197  0.002 0.2
## 198 -0.001 1.0
## 199 -0.001 0.6
## 200  0.001 1.0
## 201  0.005 0.0
## 202  0.000 1.0
## 203  0.000 0.2
## 204 -0.003 0.0
## 205  0.000 0.8
## 206  0.000 0.8
## 207  0.002 0.0
## 208  0.002 0.2
## 209 -0.001 0.4
## 210 -0.009 0.0
## 211  0.001 1.0
## 212  0.000 0.4
## 213  0.001 0.4
## 214 -0.001 0.4
## 215 -0.001 0.8
## 216 -0.004 0.2
## 217 -0.002 0.0
## 218  0.001 0.8
## 219  0.002 0.0
## 220  0.002 0.4
## 221  0.001 0.6
## 222 -0.001 0.0
## 223  0.002 0.0
## 224 -0.001 1.0
## 225 -0.004 0.4
## 226  0.002 0.2
## 227  0.003 0.2
## 228  0.000 0.6
## 229 -0.003 0.0
## 230 -0.002 0.8
## 231 -0.001 0.6
## 232  0.000 1.0
## 233  0.000 0.6
## 234 -0.001 0.4
## 235  0.002 0.2
## 236  0.007 0.2
## 237  0.003 0.0
## 238 -0.002 0.0
## 239 -0.003 0.0
## 240  0.000 0.8
## 241  0.000 1.0
## 242  0.001 0.8
## 243  0.001 0.6
## 244  0.000 0.8
## 245 -0.003 0.4
## 246 -0.001 0.4
## 247  0.001 0.6
## 248  0.001 0.6
## 249  0.000 1.0
## 250 -0.001 1.0
## 251 -0.003 0.0
## 252  0.000 1.0
## 253  0.003 0.0
## 254 -0.001 0.8
## 255 -0.004 0.0
## 256 -0.003 0.4
## 257 -0.002 0.8
## 258  0.000 0.8
## 259  0.002 0.4
## 260  0.003 0.6
## 261  0.002 0.4
## 262  0.002 0.2
## 263 -0.001 0.4
## 264 -0.003 0.0
## 265  0.002 0.2
## 266  0.005 0.0
## 267  0.002 0.0
## 268  0.000 0.8
## 269 -0.003 0.0
## 270 -0.002 0.6
## 271  0.002 0.6
## 272  0.002 0.0
## 273 -0.001 0.2
## 274  0.000 1.0
## 275 -0.003 0.0
## 276  0.000 1.0
## 277  0.001 0.8
## 278  0.001 0.6
## 279 -0.001 0.4
## 280  0.000 0.8
## 281  0.000 1.0
## 282  0.000 1.0
## 283  0.000 1.0
## 284  0.000 1.0
## 285  0.000 1.0
## 286  0.000 1.0
## 287  0.000 1.0
## 288  0.000 1.0
## 289  0.000 1.0
## 290  0.000 1.0
## 291  0.061 0.2
## 292  0.028 0.2
## 293 -0.040 0.0
## 294  0.010 1.0
## 295 -0.043 0.4
## 296  0.031 0.0
## 297  0.014 0.2
## 298 -0.008 0.0
## 299 -0.013 0.0
## 300 -0.015 0.2
## 301 -0.007 1.0
## 302  0.002 0.8
## 303  0.011 0.0
## 304 -0.006 0.2
## 305 -0.016 0.2
## 306 -0.008 0.4
## 307  0.003 0.6
## 308  0.003 0.6
## 309 -0.002 0.8
## 310 -0.001 0.6
## 311  0.015 0.0
## 312  0.008 0.2
## 313 -0.002 0.4
## 314 -0.010 0.0
## 315 -0.008 0.4
## 316  0.000 0.6
## 317  0.008 0.4
## 318  0.003 1.0
## 319 -0.005 0.2
## 320 -0.014 0.2
## 321  0.003 0.0
## 322 -0.001 0.8
## 323  0.004 0.6
## 324 -0.004 0.2
## 325 -0.003 0.0
## 326  0.002 0.4
## 327 -0.003 0.8
## 328 -0.002 0.4
## 329  0.005 0.2
## 330 -0.003 0.8
## 331  0.020 0.0
## 332  0.000 0.4
## 333 -0.005 0.2
## 334 -0.006 0.6
## 335  0.003 0.4
## 336  0.003 0.6
## 337 -0.005 0.4
## 338 -0.002 0.6
## 339  0.004 0.2
## 340  0.004 0.6
## 341  0.002 0.6
## 342  0.000 1.0
## 343 -0.004 0.2
## 344  0.005 0.8
## 345  0.000 0.6
## 346  0.019 0.0
## 347 -0.001 0.8
## 348 -0.005 0.2
## 349 -0.003 0.2
## 350  0.001 1.0
## 351  0.016 0.0
## 352 -0.003 0.8
## 353 -0.001 0.6
## 354 -0.001 1.0
## 355 -0.009 0.4
## 356  0.019 0.2
## 357 -0.002 0.4
## 358 -0.005 0.4
## 359 -0.007 0.4
## 360  0.012 0.2
## 361  0.013 0.0
## 362  0.015 0.0
## 363 -0.005 0.0
## 364 -0.014 0.0
## 365 -0.001 0.6
## 366  0.018 0.0
## 367  0.008 0.4
## 368 -0.009 0.0
## 369 -0.009 0.2
## 370  0.008 0.2
## 371  0.013 0.0
## 372  0.008 0.0
## 373 -0.010 0.0
## 374 -0.004 0.0
## 375  0.006 0.4
## 376  0.005 1.0
## 377 -0.003 0.6
## 378 -0.004 1.0
## 379  0.002 1.0
## 380  0.008 0.8
## 381  0.006 0.8
## 382  0.005 0.2
## 383  0.001 0.8
## 384 -0.005 0.2
## 385 -0.011 0.4
## 386  0.001 0.8
## 387  0.001 0.8
## 388 -0.007 0.6
## 389  0.004 0.6
## 390  0.008 0.6
## 391 -0.002 0.4
## 392  0.005 0.4
## 393  0.002 0.4
## 394  0.000 0.6
## 395 -0.013 0.0
## 396  0.022 0.0
## 397 -0.002 0.6
## 398 -0.008 0.0
## 399 -0.001 1.0
## 400  0.005 0.8
## 401 -0.009 0.4
## 402 -0.011 0.0
## 403  0.002 0.6
## 404  0.008 0.2
## 405  0.012 0.0
## 406 -0.003 0.4
## 407 -0.002 1.0
## 408  0.002 0.2
## 409  0.003 0.8
## 410 -0.004 0.8
## 411 -0.008 0.4
## 412 -0.006 0.2
## 413  0.006 0.0
## 414  0.005 0.4
## 415 -0.006 0.4
## 416 -0.002 0.8
## 417  0.008 0.0
## 418  0.002 0.2
## 419 -0.007 0.2
## 420 -0.007 0.6
## 421  0.002 0.4
## 422  0.000 0.8
## 423  0.004 0.4
## 424  0.000 0.8
## 425 -0.013 0.6
## 426  0.000 0.8
## 427  0.000 0.8
## 428  0.004 0.2
## 429 -0.007 0.0
## 430  0.004 0.8
## 431 -0.027 0.0
## 432 -0.007 0.2
## 433  0.008 0.0
## 434  0.008 0.0
## 435  0.006 0.4
## 436  0.000 1.0
## 437  0.000 1.0
## 438  0.000 1.0
## 439  0.000 1.0
## 440  0.000 1.0
## 441  0.000 1.0
## 442  0.000 1.0
## 443  0.000 1.0
## 444  0.000 1.0
## 445  0.000 1.0
## 446  0.006 0.0
## 447 -0.004 0.2
## 448 -0.004 0.8
## 449  0.002 0.0
## 450  0.011 0.2
## 451 -0.065 0.8
## 452  0.010 1.0
## 453  0.037 0.2
## 454  0.006 0.8
## 455 -0.071 0.4
## 456 -0.071 0.8
## 457  0.010 1.0
## 458  0.040 0.2
## 459  0.007 0.8
## 460 -0.077 0.4
## 461 -0.016 0.0
## 462  0.012 0.4
## 463  0.012 0.8
## 464 -0.005 0.0
## 465 -0.029 0.2
## 466  0.006 0.4
## 467 -0.002 0.8
## 468 -0.004 0.8
## 469  0.000 0.6
## 470  0.008 0.4

6 Sensitivity Analyses

In the manuscript, several sensitivity analyses are proposed:

  1. Differences (CFA/EFA) in effects across data collected only at UM site.
  2. Resampling of CFA/EFA in effects across larger ABCD data to evaluate the stability of model effects

6.1 UM Specific CFA/ESEM/EFA

In the chunk below, the PDS simulated data will be used as the filter, assuming that PDS 3 are the values reflecting the site of interest.

ABCD_site_spec <- sim_ABCD_data %>% filter(PDS == 3)

sim_AHRB_data$PDS <- NA
sim_MLS_data$PDS <- NA

UM_site_spec <- rbind(sim_AHRB_data,
                      sim_MLS_data,
                      ABCD_site_spec # UM specified ABCD data
                      )

6.1.1 CFA

UM_all_sample <- cfa(model = MID_model, data = UM_site_spec,
               estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

UM_config_cfa <- cfa(model = MID_model, data = UM_site_spec, group = 'set', 
                      estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

UM_metric_cfa <-cfa(model = MID_model, data = UM_site_spec, 
                 group = 'set', group.equal=c("loadings"),
                 estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

UMsite_out <- matrix(NA, ncol = 9, nrow = 3)
colnames(UMsite_out) <- c("model","chisq","df","pvalue", "rmsea", "cfi", "srmr",
                   "AIC", "BIC")

# save fit measures from models
UMsite_out[1,2:7] <- round(data.matrix(fitmeasures(UM_all_sample, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                    digits=3)

UMsite_out[2,2:7] <- round(data.matrix(fitmeasures(UM_config_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                            digits=3)

UMsite_out[3,2:7] <- round(data.matrix(fitmeasures(UM_metric_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                    digits=3)

UMsite_out[1,8] <- round(AIC(UM_all_sample),3)
UMsite_out[2,8] <- round(AIC(UM_config_cfa),3)
UMsite_out[3,8] <- round(AIC(UM_metric_cfa),3)

# BIC models
UMsite_out[1,9] <- round(BIC(UM_all_sample),3)
UMsite_out[2,9] <- round(BIC(UM_config_cfa),3)
UMsite_out[3,9] <- round(BIC(UM_metric_cfa),3)

UMsite_out[1:3,1] <-  c("Overall CFA", "Config MG-CFA", "Metric MG-CFA")


UMsite_out %>% 
  knitr::kable(
    caption = "Fit statistics from MG-CFA and ESEM models",
    booktabs = TRUE
    )
Fit statistics from MG-CFA and ESEM models
model chisq df pvalue rmsea cfi srmr AIC BIC
Overall CFA 1167.367 349 0 0.065 0.665 0.057 -9462.261 -9094.083
Config MG-CFA 1915.884 1047 0 0.067 0.654 0.073 -9275.648 -8171.115
Metric MG-CFA 1974.859 1099 0 0.065 0.651 0.078 -9320.674 -8441.379

6.1.2 EFA

In this case, only the data for the ABCD sample changes (reduced from 21 –> 1 site [UM]). Hence, rerunning only the ABCD EFA. Factor congruence estimation will use EFA from above for AHRB and MLS.

UM_abcd_efadata = subset(UM_site_spec[,c("AWin_v_Neut_L_NAcc_run1"  ,"AWin_v_Neut_L_NAcc_run2" ,
                         "BWin_v_Neut_L_NAcc_run1"  ,"BWin_v_Neut_L_NAcc_run2" ,
                         "BWin_v_BLose_L_NAcc_run1" ,"BWin_v_BLose_L_NAcc_run2",
                          "AWin_v_Neut_R_NAcc_run1" , "AWin_v_Neut_R_NAcc_run2",
                          "BWin_v_Neut_R_NAcc_run1" , "BWin_v_Neut_R_NAcc_run2",
                          "BWin_v_BLose_R_NAcc_run1", "BWin_v_BLose_R_NAcc_run2",
                         # insula values apprach 
                         "AWin_v_Neut_R_Insula_run1","AWin_v_Neut_R_Insula_run2", 
                         "BWin_v_Neut_R_Insula_run1","BWin_v_Neut_R_Insula_run2", 
                         # avoidance
                         "ALose_v_Neut_L_Insula_run1","ALose_v_Neut_L_Insula_run2",
                         "BLose_v_Neut_L_Insula_run1","BLose_v_Neut_L_Insula_run2",
                         "BLose_v_BWin_L_Insula_run1","BLose_v_BWin_L_Insula_run2",
                         "ALose_v_Neut_R_Insula_run1","ALose_v_Neut_R_Insula_run2",
                         "BLose_v_Neut_R_Insula_run1","BLose_v_Neut_R_Insula_run2",
                         "BLose_v_BWin_R_Insula_run1","BLose_v_BWin_R_Insula_run2",
                         "set")] %>% filter(set==1))
paran(x = UM_abcd_efadata[,1:28],
      iterations = 1000, quietly = FALSE, centile = 95, 
      status = FALSE, all = TRUE, cfa = TRUE, graph = TRUE, color = TRUE, 
      col = c("black", "red", "blue"), lty = c(1, 2, 3), lwd = 1, legend = TRUE, 
      seed = 100)
## 
## Using eigendecomposition of correlation matrix.
## 
## Results of Horn's Parallel Analysis for factor retention
## 1000 iterations, using the 95 centile estimate
## 
## -------------------------------------------------- 
## Factor      Adjusted    Unadjusted    Estimated 
##             Eigenvalue  Eigenvalue    Bias 
## -------------------------------------------------- 
## No components passed. 
## -------------------------------------------------- 
## 1           3.628570    4.436251      0.807681
## 2           0.397564    1.102327      0.704762
## 3           0.192784    0.810407      0.617622
## 4           0.246962    0.798866      0.551903
## 5           0.142275    0.636878      0.494602
## 6           0.188467    0.627145      0.438678
## 7           0.179993    0.569582      0.389589
## 8           0.102263    0.445540      0.343277
## 9           0.063590    0.363779      0.300188
## 10          0.051445    0.311718      0.260272
## 11          0.060812    0.280569      0.219757
## 12          0.041416    0.222636      0.181219
## 13          0.038991    0.183582      0.144591
## 14          0.042094    0.149378      0.107284
## 15         -0.062117    0.011462      0.073580
## 16         -0.066274   -0.02475      0.041519
## 17         -0.073236   -0.06771      0.005522
## 18         -0.065103   -0.09174     -0.02664
## 19         -0.048208   -0.10881     -0.06060
## 20         -0.081346   -0.17265     -0.09130
## 21         -0.063693   -0.18635     -0.12266
## 22         -0.069725   -0.22210     -0.15238
## 23         -0.054965   -0.23672     -0.18176
## 24         -0.035486   -0.24929     -0.21380
## 25         -0.027979   -0.27179     -0.24381
## 26         -0.038075   -0.31251     -0.27444
## 27         -0.013812   -0.32266     -0.30885
## 28          0.011275   -0.33361     -0.34489
## -------------------------------------------------- 
## 
## Adjusted eigenvalues > 0 indicate dimensions to retain.
## (14 factors    retained)

plot(nScree(x=UM_abcd_efadata[,1:28],model="factors"))

UM_abcd_efa <- factanal(x = UM_abcd_efadata[,1:28],  #raw data  
              factors = 2, rotation = "promax" # oblique rotation allow for non-orthogonal structure
              )

heatmaply(round(UM_abcd_efa$loadings[,1:2],2) %>% print(sort = T),
          scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
                 low = "blue", 
                 high = "darkred", 
                 space = "Lab",
                 midpoint = 0, 
                 limits = c(-1, 1)
               ),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 9, fontsize_col = 9,
               labCol = colnames(UM_abcd_efa$loadings[,1:2]),
               labRow = rownames(UM_abcd_efa$loadings[,1:2]),
               heatmap_layers = theme(axis.line=element_blank()),
          
)
##                            Factor1 Factor2
## AWin_v_Neut_L_NAcc_run1      -0.10    0.36
## AWin_v_Neut_L_NAcc_run2      -0.19    0.33
## BWin_v_Neut_L_NAcc_run1       0.02    0.51
## BWin_v_Neut_L_NAcc_run2      -0.17    0.28
## BWin_v_BLose_L_NAcc_run1     -0.25    0.29
## BWin_v_BLose_L_NAcc_run2     -0.16    0.31
## AWin_v_Neut_R_NAcc_run1       0.15    0.59
## AWin_v_Neut_R_NAcc_run2       0.21    0.71
## BWin_v_Neut_R_NAcc_run1       0.03    0.42
## BWin_v_Neut_R_NAcc_run2      -0.09    0.33
## BWin_v_BLose_R_NAcc_run1     -0.01    0.44
## BWin_v_BLose_R_NAcc_run2      0.06    0.53
## AWin_v_Neut_R_Insula_run1    -0.23    0.02
## AWin_v_Neut_R_Insula_run2    -0.02    0.22
## BWin_v_Neut_R_Insula_run1    -0.01    0.27
## BWin_v_Neut_R_Insula_run2    -0.21    0.20
## ALose_v_Neut_L_Insula_run1    0.38   -0.03
## ALose_v_Neut_L_Insula_run2    0.38   -0.04
## BLose_v_Neut_L_Insula_run1    0.45   -0.03
## BLose_v_Neut_L_Insula_run2    0.41    0.00
## BLose_v_BWin_L_Insula_run1    0.52    0.02
## BLose_v_BWin_L_Insula_run2    0.56    0.13
## ALose_v_Neut_R_Insula_run1    0.54    0.03
## ALose_v_Neut_R_Insula_run2    0.69    0.11
## BLose_v_Neut_R_Insula_run1    0.42   -0.08
## BLose_v_Neut_R_Insula_run2    0.42   -0.04
## BLose_v_BWin_R_Insula_run1    0.33    0.18
## BLose_v_BWin_R_Insula_run2    0.35    0.18
fa.congruence(x = list(UM_abcd_efa, mls_efa, ahrb_efa), digits = 2) %>% 
  knitr::kable(
    col.names = c("1. ABCD F1", "2. ABCD F2", 
                  "3. MLS F1", "4. MLS F2","5. MLS F3",
                  "6. AHRB F1", "7. AHRB F2","8. AHRB F3", "8. AHRB F4"),
    caption = "ABCD, MLS and AHRB EFA Factor Congruence",
    booktabs = TRUE
    )
ABCD, MLS and AHRB EFA Factor Congruence
1. ABCD F1 2. ABCD F2 3. MLS F1 4. MLS F2 5. MLS F3 6. AHRB F1 7. AHRB F2 8. AHRB F3 8. AHRB F4
Factor1 1.00 0.05 -0.10 0.79 0.44 0.66 -0.25 0.06 0.69
Factor2 0.05 1.00 0.89 0.12 0.14 -0.15 0.57 0.48 0.08
Factor1 -0.10 0.89 1.00 0.07 0.15 -0.21 0.68 0.38 -0.01
Factor2 0.79 0.12 0.07 1.00 0.05 0.51 -0.07 0.02 0.67
Factor3 0.44 0.14 0.15 0.05 1.00 0.37 0.13 0.00 0.34
Factor1 0.66 -0.15 -0.21 0.51 0.37 1.00 -0.06 0.17 0.22
Factor2 -0.25 0.57 0.68 -0.07 0.13 -0.06 1.00 -0.12 -0.09
Factor3 0.06 0.48 0.38 0.02 0.00 0.17 -0.12 1.00 -0.13
Factor4 0.69 0.08 -0.01 0.67 0.34 0.22 -0.09 -0.13 1.00

6.2 Resampling ABCD CFA/EFA

abcd_resamp_df <- subset(brain_set[,c("AWin_v_Neut_L_NAcc_run1"  ,"AWin_v_Neut_L_NAcc_run2" ,
                         "BWin_v_Neut_L_NAcc_run1"  ,"BWin_v_Neut_L_NAcc_run2" ,
                         "BWin_v_BLose_L_NAcc_run1" ,"BWin_v_BLose_L_NAcc_run2",
                          "AWin_v_Neut_R_NAcc_run1" , "AWin_v_Neut_R_NAcc_run2",
                          "BWin_v_Neut_R_NAcc_run1" , "BWin_v_Neut_R_NAcc_run2",
                          "BWin_v_BLose_R_NAcc_run1", "BWin_v_BLose_R_NAcc_run2",
                         # insula values apprach 
                         "AWin_v_Neut_R_Insula_run1","AWin_v_Neut_R_Insula_run2", 
                         "BWin_v_Neut_R_Insula_run1","BWin_v_Neut_R_Insula_run2", 
                         # avoidance
                         "ALose_v_Neut_L_Insula_run1","ALose_v_Neut_L_Insula_run2",
                         "BLose_v_Neut_L_Insula_run1","BLose_v_Neut_L_Insula_run2",
                         "BLose_v_BWin_L_Insula_run1","BLose_v_BWin_L_Insula_run2",
                         "ALose_v_Neut_R_Insula_run1","ALose_v_Neut_R_Insula_run2",
                         "BLose_v_Neut_R_Insula_run1","BLose_v_Neut_R_Insula_run2",
                         "BLose_v_BWin_R_Insula_run1","BLose_v_BWin_R_Insula_run2",
                         "set")] %>% filter(set==1))

For resampling of the CFA model, using bootstrapLavaan for lavaan. First fitting the cfa model, then creating 1000 bootstrapped sampled and extracting fit statistics

set.seed(1111)
boot_cfa <- cfa(model = MID_model, data = abcd_resamp_df,
                 estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

out_cfaboot <- bootstrapLavaan(object = boot_cfa, R = 1000, 
                               FUN = fitMeasures,
                               fit.measures=c("chisq","rmsea","cfi",
                                              "tli","srmr","AIC","BIC"),
                               parallel="multicore", ncpus=4)

cfaboot_df <- data.frame(out_cfaboot)

For the resampling of the EFA model, using sample_n to get [1000] samples of N = 1000 (w/ replacement) of ABCD data. Then, estimating recommended N of factors per paralell analysis. Saving this to dataframe

# create empty df where data will be saved and compiled for models
#resampled_cfa <- matrix(NA, ncol = 11, nrow = 50) # resampling 50x for Config + #Metric models
#colnames(resampled_cfa) <- c("Sample",
#                              "chisq","df","pvalue", 
#                              "rmsea","cfi","tli","srmr","AIC","BIC","Factors")
#
#n_loop = 50

resampled_cfa <- matrix(NA, ncol = 2, nrow = 1000) # resampling 50x for Config + Metric models
colnames(resampled_cfa) <- c("Sample","Factors")

samples = 1000
  
for (s in 1:samples) {
  
  sub_df <- sample_n(tbl = abcd_resamp_df, size = 1000, replace = TRUE)
  
  resampled_cfa[s,1] <- s

  val <- nScree(x=sub_df[,1:28],model="factors")
  resampled_cfa[s,2] <- as.integer(val$Components[3])
  


}

resampled_res <- data.frame(resampled_cfa)

Plotting the mean + 95% Confidence interval of values

n = 1000

ci_plt1 <- cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         srmr,rmsea) %>% 
  dplyr::group_by(FitIndex) %>% 
  dplyr::summarize(m = mean(Statistic), stdev = sd(Statistic)) %>% 
  ggplot(aes(x =FitIndex, y = m, fill = FitIndex, color=FitIndex)) +
  geom_point()+
  geom_errorbar(aes(ymin=m-(1.96*stdev/sqrt(n)),
                    ymax=m+(1.96*stdev/sqrt(n))), 
                width=.2,
                position=position_dodge(0.05))+
  labs(
    title = 'CFA: RMSEA & SRMR',
    x = 'Fit Stats',
    y = 'Type',
  )+
  theme_minimal()


ci_plt2 <- cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         cfi,tli) %>% 
  dplyr::group_by(FitIndex) %>% 
  dplyr::summarize(m = mean(Statistic), stdev = sd(Statistic)) %>% 
  ggplot(aes(x =FitIndex, y = m, fill = FitIndex, color=FitIndex)) +
  geom_point()+
  geom_errorbar(aes(ymin=m-(1.96*stdev/sqrt(n)),
                    ymax=m+(1.96*stdev/sqrt(n))), 
                width=.2,
                position=position_dodge(0.05))+
  labs(
    title = 'CFA: CFI & TLI',
    x = 'Fit Stats',
    y = 'Type',
  )+
  theme_minimal()


ci_plt3 <- cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         aic,bic) %>% 
  dplyr::group_by(FitIndex) %>% 
  dplyr::summarize(m = mean(Statistic), stdev = sd(Statistic)) %>% 
  ggplot(aes(x =FitIndex, y = m, fill = FitIndex, color=FitIndex)) +
  geom_point()+
  geom_errorbar(aes(ymin=m-(1.96*stdev/sqrt(n)),
                    ymax=m+(1.96*stdev/sqrt(n))), 
                width=.2,
                position=position_dodge(0.05))+
  labs(
    title = 'CFA: AIC & BIC',
    x = 'Fit Stats',
    y = 'Type',
  )+
  theme_minimal()


ci_plt4 = resampled_res %>%
  dplyr::summarize(m = mean(Factors), stdev = sd(Factors)) %>% 
  ggplot(aes(x ="", y = m)) +
  geom_point()+
  geom_errorbar(aes(ymin=m-(1.96*stdev/sqrt(n)),
                    ymax=m+(1.96*stdev/sqrt(n))), 
                width=.2,
                position=position_dodge(0.05))+
  ylim(0,5)+
  labs(
    title = 'EFA Factors',
    x = '',
    y = 'Number of Factors',
  )+
  theme_minimal()

ci_plt1;ci_plt2;ci_plt3;ci_plt4

Plotting the distribution of values

plt1 <- cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         srmr,rmsea) %>% 
  ggplot(aes(x =FitIndex, y = Statistic, fill = FitIndex, color=FitIndex)) +
  ggdist::stat_halfeye(adjust = .5, width = .7, .width = 0, justification = -.2, 
                       point_colour = NA, alpha = .5) +
  geom_boxplot(width = .2, outlier.shape = NA, alpha = .3) + 
  geom_jitter(width = .05, alpha = .5) +
  theme_minimal()+
  labs(
    title = 'CFA: RMSEA & SRMR',
    x = 'Fit Stats',
    y = 'Type',
  )

plt2 = cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         cfi,tli) %>% 
  ggplot(aes(x =FitIndex, y = Statistic, fill = FitIndex, color=FitIndex)) +
  ggdist::stat_halfeye(adjust = .5, width = .7, .width = 0, justification = -.2, 
                       point_colour = NA, alpha = .5) +
  geom_boxplot(width = .2, outlier.shape = NA, alpha = .3) + 
  geom_jitter(width = .05, alpha = .5) +
  theme_minimal()+
  labs(
    title = 'CFA: CFI & TLI',
    x = 'Fit Stats',
    y = 'Type',
  )


plt3 = cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         aic,bic) %>% 
  ggplot(aes(x =FitIndex, y = Statistic, fill = FitIndex, color=FitIndex)) +
  ggdist::stat_halfeye(adjust = .5, width = .7, .width = 0, justification = -.2, 
                       point_colour = NA, alpha = .5) +
  geom_boxplot(width = .2, outlier.shape = NA, alpha = .3) + 
  geom_jitter(width = .05, alpha = .5) +
  theme_minimal()+
  labs(
    title = 'CFA: AIC & BIC',
    x = 'Fit Stats',
    y = 'Type',
  )


avg = round(mean(resampled_res$Factors),1)
minimum = min(resampled_res$Factors)
maximum = max(resampled_res$Factors)

plt4 = resampled_res %>%
  ggplot(aes(x ="", y = Factors)) +
  ggdist::stat_halfeye(adjust = .5, width = .7, .width = 0, justification = -.2, 
                       point_colour = NA, alpha = .5) +
  geom_jitter(width = .05, alpha = .5) +
  theme_minimal()+
  labs(
    title = 'EFA: Parallel Analysis Recommended Factors',
    subtitle = paste("Mean: ",avg," [Min: ", minimum, "Max:", maximum,"]"),
    x = 'Fit Stats',
    y = 'Type',
  )

plt1;plt2;plt3;plt4